Physical parameter optimization and band alignment approach for efficiency improvement in Cs₂AgBiBr₆ based lead-free perovskite solar cells

Abstract

In recent years, organic-inorganic halide perovskite solar cells (PSCs) have garnered significant global attention due to their exceptional performance and high-power conversion efficiency (PCE). The impressive device capabilities have encouraged extensive research into various advanced engineering strategies aimed at improving the physical characteristics of PSCs. Nevertheless, while lead-based PSCs have achieved outstanding PCEs, concerns regarding lead toxicity and long-term stability hinder their commercial viability. Besides, an appropriate hole transport material is also required to reduce the recombination losses at interfaces. In the present study, PSCs were designed in SCAPS simulation software with cell configuration of FTO/TiO₂/Cs₂AgBiBr₆/HTLs (CuI, CuSCN, Cu₂O, Spiro-OMeTAD)/Au. Here, lead-free stable double perovskite material Cs₂AgBiBr₆ is used as light absorbing material and TiO₂ electron transport material. However, device response of PSCs is studied with different hole transport materials. With optimization of defects, and thickness of perovskite absorber, along with operating temperature and series resistance, Cu₂O as hole transport layer (HTL) based PSCs have achieved open-circuit voltage (V_OC) of 1.33 V, current density of (J_SC) of 8.78 mA/cm², fill factor (FF) of 64.96%, and PCE of 7.60%. The reason behind the variation in device performance was realised using capacitance-voltage (C-V), conductance-voltage (G-V), capacitance – frequency (C-f) and, conductance-frequency (G-f) analysis. It has been found that Cu₂O HTL-based PSCs exhibited reduced defects at the interfacial region, attributed to the appropriate band alignment with the Cs₂AgBiBr₆ perovskite absorber. The suggested simulation study may contribute significantly to the advancement of lead-free all-inorganic PSCs, aiming for improved efficiency.

Introduction

The rapid increase in world energy consumption has prompted a global competition to identify alternative fuels that depend on renewable energy sources¹. The solar light is considered as a sustainable and environmentally friendly energy source, enhancing ecological conditions while providing electricity for future industrial applications². Nowadays various types of photovoltaic technology have gained superior PCE for instance, cadmium telluride thin films have recently achieved enhanced efficiencies of up to 22%³, while solar cells utilizing copper indium gallium selenide have reached an efficiency of more than 22%⁴. Additionally, a novel category of lead hybrid PSCs has emerged, with efficiencies increasing to more than 26% in recent years⁵. PSCs are recognized as among the most efficient solar cells available, owing to their remarkable competence to convert light into electrical energy. However, the lead component in PSCs is the hurdle of this attractive technology⁶. It is advisable to replace the toxic lead components in lead halide perovskites with environmentally friendly materials to develop solar cells that are both highly efficient and cost-effective⁷. Now a days, double perovskite absorber based solar cells are more popular compared to single perovskite bases solar cells. The major difference between double perovskites and single perovskites is found in their composition, stability, toxicity, and efficiency. Single perovskites, such as MAPbI₃ and CsPbBr₃, feature a straightforward structure with a divalent metal cation such as Pb²⁺ or Sn²⁺, which results in high efficiency. However, they face the issues of poor stability and lead toxicity. On the other hand, double perovskites, exemplified by Cs₂AgBiBr₆, substitute lead with two different cations such as Ag⁺ and Bi³⁺, enhancing their stability and making them more environment friendly, although they typically possess an indirect bandgap or nearly 2 eV, which reduces their absorption and efficiency^6,8,9,10. Various experimental and theoretical studies have reported the potential of this material for photovoltaic applications. Gruel et al., incorporated Cs₂AgBiBr₆ in PSC device for the first time. The X-ray diffraction measurement revealed that at least 250ºC of temperature is required to transform precursor into Cs₂AgBiBr₆ film without any additional phase. Photoluminescence measurements indicate that the films exhibit absorption characteristics and lifetimes of the photoexcited species that are comparable to those of lead-based materials. The champion PCE of 1.66% and 2.43% are obtained for forward and backward scan respectively¹¹. Wu et al. fabricated a Cs₂AgBiBr₆ based PSCs using low-pressure assisted solution technique under ambient atmospheric conditions and delivered maximum PCE of 1.44%. The Cs₂AgBiBr₆ film shows the cell unit parameter of a = 11.2640(8) Å contains the space group Fm-3 m, and the bandgap of 2.05 eV. The device exhibited the open circuit voltage (V_OC) of 1.04 V¹². Zang et al. reported that the hydrogenation can reduced the bandgap of PSCs from 2.18 eV to 1.64 eV of Cs₂AgBiBr₆ based absorber. The efficiency of PSCs improved from 4.23–6.37%¹³. Recently, Hasan and his team doped polypyrrole (PPy) in Cs₂AgBiBr₆ perovskite absorber and prepared the material using sol-gel technique. The X-ray diffraction spectra confirmed the increase in grain size up to 34 nm and reduction in bandgap from 1.89 eV to 1.85 eV with incorporation of PPy doping. The PSCs were designed with cell configuration of glass/FTO/TiO₂/Cs₂AgBiBr₆/Spiro-OMeTAD/Au and exhibited the device efficiency of 3.51%¹⁴. The doping in Cs₂AgBiBr₆ can improve the crystallinity of the film and modulate the absorbance of the material. Pang et al. doped the Li⁺ and Na⁺ ions in the Cs₂AgBiBr₆ absorber and improved the device efficiency of perovskite solar cells. The co-doped absorber-based PSCs delivered device efficiency of 5.02% with current density of 6.56 mA/cm²¹⁵. Xiao et al. developed a Cs₂AgBiBr₆ film having large grain, smooth surface using sequential vapour deposition techniques. The Cu₂O HTL is deposited on perovskite absorber, and it offered suitable energy alignment and good electrical properties delivered maximum PCE of 1.52% with V_OC of 1.198 V. The obtained device output with Cu₂O HTL is superior compared to spiro-OMeTAD based HTL. This study paves the way for the continued advancement and enhancement of all-inorganic lead-free perovskite solar cells¹⁶.

Along with experimental studies various theoretical results are also reported for Cs₂AgBiBr₆ and achieved remarkable efficiency which shows its potential in photovoltaic devices. Uddin et al. reported combined DFT and SCPAS simulation study of PSCs using different electron transport layers (ETLs) and hole transport layers (HTLs). With optimization of various parameters such as thickness of ETLs, absorber and ETLs, series resistance, temperature etc., the PSC exhibited maximum PCE of 23.5% for cell configuration of FTO/AZnO/Cs₂AgBiBr₆/CNTS/Au¹⁷. In our previous study, the combined DFT and SCPAS simulation study was performed using WIEN2k and SCAPS simulation software. The DFT revealed the optimized band gap of 2.08 eV of Cs₂AgBiBr₆. The PSCs was designed with cell configurations of FTO/TiO₂/Cs₂AgBiBr₆/Spiro-OMeTAD/Au and superior PCE of 6.68% was achieved using proper optimization of bandgap, defect density, thickness of absorber, series resistance and operating temperature¹⁸.

In the present study, we have successfully evaluated the performance of Cs₂AgBiBr₆ based PSCs using different HTLs (CuI, CuSCN, Cu₂O, Spiro-OMeTAD) through SCAPS based simulations techniques and achieved enhance device efficiency with just optimization of absorber thickness and temperature. Subsequently, the capacitance-voltage (C-V), conductance-voltage (G-V) measurements, capacitance-frequency (C-f), conductance frequency (G-f) characteristics, and Nyquist plots are analysed to investigate the variation in the performance of devices based on Cs₂AgBiBr₆ PSCs.

Simulation details

The present study unitized the solar cell capacitance simulator (SCPAS) software. The PSCs with cell configurations of FTO/TiO₂/Cs₂AgBiBr₆/HTLs/Au was designed to investigate and optimize various physical parameters. The simulation focussed on evaluating the performance of PSCs that employed the lead-free double perovskite Cs₂AgBiBr₆ as the light-absorbing material, titanium dioxide (TiO₂) as the electron transport layer (ETL), and four distinct HTLs such as CuI, CuSCN, Cu₂O, and spiro-OMeTAD. Gold (Au) served as the back electrode material and fluorine doped tin oxide (FTO) as a front electrode. The analysis involved the device structure and the I-V characteristics of the simulated PSCs. Figure 1(a, b) illustrates device structure and energy band diagram of simulated device. The I-V curve alongside the quantum efficiency (QE), (depicted as an inset), is shown in Fig. 1(c). The different parameters used for this simulation studies are collected from various reported literature as demonstrated in Tables 1, 2 and 3^{11,18,19,20,21,22,23}. The PSCs were initially optimized, as demonstrated in Table 4, and the findings were in strong alignment with the experimental results. Furthermore, I-V and QE curves for PSCs with various HTL materials were analysed to assess their light-harvesting efficiency throughout the solar spectrum without optimization of any physical parameters as show in in Fig. 2(a, b). The Cu₂O shows highest V_OC and J_SC and spiro-OMeTAD shows lower V_OC and J_SC for the simulated PSCs. In Fig. 2 (b), the reported device has ability to absorb the light in lower wavelength rang. It has large band gap which limit the light absorption. The bandgap of a material evaluated the specific wavelengths of light it is capable of absorbing. The energy band diagrams of the PSCs with different HTLs are shown in Fig. 3. The simulations indicate that CuSCN and Cu₂O exhibit favourable alignment for effective hole transport material, while Spiro-OMeTAD, despite its common usage, could present additional energetic barriers owing to its significant valence band offset. The interaction occurring at the interfacial point between two layers significantly influences the performance of the device. Two interfacial defects at ETL/perovskite and perovskite/HTL are considered during study. The total defect density, capture cross section, and energy level with respect to E_v is illustrated in Table 2. This study employs the optical absorption constant (α) derived from the absorption sub-models based on the sqrt (hν - Eg) law, as established in the traditional SCAPS framework within the SCAPS software. These simulations allowed valuable understandings into the appropriateness of different HTL materials for optimizing the PCE, stability, and overall performance of the lead-free Cs₂AgBiBr₆-based lead-free PSCs.

Fig. 1

(a) Device configuration of PSCs, (b) energy band diagram of different materials used in PSCs, (c) I-V and QE curve (Inset) of simulated PSCs with cell configuration of FTO/TiO₂/Cs₂AgBiBr₆/Spiro-OMeTAD/Au.

Table 1 Input parameters of different materials used to simulate PSCs.

Table 2 Interfacial parameters of PSCs.

Table 3 Different input parameter of HTLs in simulated PSCs.

Table 4 The initial optimized parameters of PSC with cell configuration of FTO/TiO₂/Cs₂AgBiBr₆/Spiro-OMeTAD/Au.

Fig. 2

I-V and QE characteristics of PSCs with different HTLs.

Fig. 3

Simulated energy diagram of PSCs with different HTLs.

The SCAPS-1D is a sophisticated and esteemed simulation tool created by the department of electronics and information systems at Ghent University in Belgium. This software is specifically tailored for the examination and evaluation of photovoltaic (PV) devices, serving as a robust platform for analysing and forecasting the optoelectronic characteristics of diverse solar cell configurations. With the use of fundamental physical principles, including the continuity equations for electrons and holes alongside the electrostatic potential equation, SCAPS-1D functions within a steady-state framework to replicate the performance of solar cells. These equations enable precise modelling of charge transport, recombination phenomena, and electric field distributions throughout the device. Additionally, SCAPS-1D incorporates material properties, interface modifications, and external influences such as temperature and light conditions, representing it a flexible instrument for enhancing solar cell designs²⁴.

The charge density and the electric fields (E) at the p–n junction can be related and expressed using following functions:

$$\:\frac{{\:\partial\:}^{2}\varphi\:}{{\:\partial\:}^{2}x}=-\frac{\:\partial\:\text{E}}{\:\partial\:\:x}\:=-\:\frac{\rho\:}{{\epsilon\:}_{s}}=-\:\frac{q}{{\epsilon\:}_{s}}\:[P-n+\:{N}_{D}^{+}\:\left(x\right)-\:{N}_{A}^{-}\:\left(x\right)\:\pm\:\:{N}_{def}\:\left(x\right)]$$

(1)

This above-mentioned equation contains various parameters for instance p and n represent the electron and hole density. $\:{N}_{D}^{+}\:$ and $\:{N}_{A}^{-}\:$denote the ionised donor and acceptor concentration. ρ denote the net charge density and q is the elementary charge.

Furthermore, the continuity equation for electron holes can be as follows:

$$\:-\frac{\:\partial\:{j}_{P}}{\:\partial\:\:x}+G-{U}_{p}\:\left(n,p\right)=0$$

(2)

$$\:\frac{\:\partial\:{j}_{n}}{\:\partial\:\:x}+G-{U}_{n}\left(n,p\right)=0$$

(3)

Here, $\:{j}_{P}$ and $\:{j}_{n}$ represent the hole and electron current density. $\:{U}_{p}\:\left(n,p\right)$ and $\:{U}_{n}\:\left(n,p\right)$ signify the recombination rate of holes and electrons. The current density of electron and holes can be also calculated using the equations mentioned below:

$$\:{j}_{P}=\:qn{\mu\:}_{p}E-q{D}_{p}\frac{\:\partial\:p}{\:\partial\:\:x}$$

(4)

$$\:{j}_{n}=\:qn{\mu\:}_{n}E+q{D}_{n}\frac{\:\partial\:n}{\:\partial\:\:x}$$

(5)

In the above-mentioned equations $\:{\mu\:}_{p}$ and $\:{\mu\:}_{n}$ represent the carrier mobility of electron and holes and $\:{D}_{p}\:\text{a}\text{n}\text{d}\:{D}_{n}$ are the diffusion coefficient of charge carrier^24,25,26,27.

Result and discussions

The band alignment approach in PSCs is essential for improving the extraction and transportation of charge carriers while minimizing energy losses, ultimately leading to enhanced device efficiency. This tactic requires the adjustment of the energy levels of the perovskite absorber in relation to the neighbouring charge transport layers, specifically the ETL and HTL to create appropriate conduction band and valence band offsets. Effective band alignment helps efficient charge separation, decreases recombination losses, and supports continuous charge transportation and ultimately enhance the device output^28,29,30. Figure 4 (a) shows the conduction and valence position of PSCs with different HTLs. Figure 4 (b) represent the charge carrier and generation and recombination of PSCs. It has been observed that the PSCs with Cu₂O shows appropriate band alignment with Cs₂AgBiBr₆ absorber compared to the PSCs with other HTLs as illustrated in Fig. 4(a). This obtained output is further supported by generation -recombination curve as Cu₂O based PSCs describes higher generation and less recombination at HTL/perovskite interfacial position as shown in Fig. 4(b).

Fig. 4

(a) Conduction band and valence band position of PSCs with different HTLs. (b) Charge carrier generation and recombination of PSCs with HTL materials.

In the simulation study, adjusting the defect density enables the examination of its influences on the performance of solar cells. Various type of defects can be considered during the evaluation of physical parameter of PSCs. However, the most common defect in PSCs is Shockley–Read–Hall (SRH) recombination model and it can be represented as:

$$\:\text{S}\text{R}\text{H}\:=\frac{n.p-{n}_{i}^{2}}{{\tau\:}_{p}.\:\:\left(n+{n}_{1}\right)+\:{\tau\:}_{n}.(p+{p}_{1})}$$

(6)

Here p₁ and n₁ defined as concentration of holes and electron in valance band and trap defects respectively.

$$n_1 = N_c.exp(\frac{{ - ({E_C} - {E_T})}}{{{K_B}.{T_L}}})$$

(7)

$$p_1 = N_v.exp(\frac{{ - ({E_T} - {E_V})}}{{{K_B}.{T_L}}})$$

(8)

$$n_{i}^{2} = n_p = n_1p_1 = N_cN_v.exp(\frac{{ - {E_g}}}{{{K_B}.{T_L}}})$$

(9)

here n and p are the concentration of charge carriers and n_i and T_L denotes the intrinsic carrier concentration and lattice temperature respectively. This Eq. (10) illustrates the electron density in thermal equilibrium related to a trap level E_T situated below the conduction band. The concentration of holes in thermal equilibrium is associated with a trap level E_T situated above the valence band as shown in Eq. (13). Equation (9) shows the product of free electron and hole concentrations equals the square of the intrinsic carrier concentration.

$$\:{\:\tau\:}_{n,p}=\:\frac{1}{{\sigma\:}_{n,p\:.\:\:}{\vartheta\:}_{th\:}.\:\:{N}_{t}}$$

(10)

The thermal velocity ($\:{\vartheta\:}_{th\:}$) is consider as 10⁺⁷ cms⁻¹ and $\:{\sigma\:}_{n,p\:}$ shows the capture cross-section of holes and electron.

Diffusion coefficient (D) and diffusion length (L) can be defined as:

$$D = \frac{{\mu .{K_B}T}}{q}$$

(11)

$$L = \sqrt{D_\tau}$$

(12)

The various symbols mentioned in above equations such as T denotes temperature in Kelvin, K_B is Boltzmann constant. The value of diffusion length of holes (L_p) and electron (L_n) can be calculated from Eqs. (10)-(12)³¹.

The impact of defect density on the performance of PSCs with different HTL is shown in Fig. 5. The various physical parameters such as V_OC, J_SC, FF and PCE is evaluated by changing its value of defect density from 1 × 10¹¹ to 1 × 10¹⁹ cm⁻³. The increase in defect density from 1 × 10¹¹ cm⁻³ the V_OC value for different HTLs is decline. The value of V_OC decreases from 1.24 V to 1.13 V for Cu₂O, 1.03 V to 0.82 V for CuSCN, 0.49 V to 0.75 V for CuI and 0.86 V to 0.66 V for spiro-OMeTAD. Similar trend has been observed in device efficiency of PSCs with different HTLs. The PCE is decreases from 6.19 to 0.22% for Cu₂O, 4.82–0.0069% for CuSCN, 4.35–0.0056% for CuI, 3.8–0.0047% for spiro-OMeTAD. It can be also observed from the trends of the graph that Cu₂O shows less recombination at higher defect density whereas more decline trends are observed in spiro-OMeTAD based PSCs. However, almost similar decline trend is observed for J_SC and FF for simulated PSCs. The PSCs exhibited superior device output of 6.19% with Cu₂O HTL at defect density of 1 × 10¹¹ cm⁻³. At lower defect density values, recombination of charge carrier reduces in PSCs, resulted in enhanced device efficiency and V_OC. Conversely, at higher defect densities, charge carrier recombination increases which leads to decrease in the diffusion lengths and carrier lifetime of both electrons and holes, ultimately resulting in diminished device output.

Fig. 5

Influence of defect density of perovskite absorber on the performance of PSCs with different HTLs.

The thickness of the light-harvesting material, commonly known as the perovskite absorber layer, is a crucial factor affecting the performance of PSCs. This parameter is essential as it affects both the efficiency of photon absorption and the movement of charge carriers³². Here, the variation in the thickness of perovskite absorber from 200 nm to 1200 nm with different HTL materials are studied and shown in Fig. 6. It can be observed that the value of V_OC, J_SC, and PCE increases with increase in thickness, however the FF reduces with increase in thickness. The maximum device efficiency of 7.05%, 5.60%, 5.05% and 4.50%; J_SC of 8.67 mA/cm², 8.47 mA/cm², 8.41 mA/cm² and 8.34 mA/cm²; FF of 63.74%, 6.21%, 6.08% and 5.99% and V_OC of 1.28 V, 1.07 V, 0.99 V and 0.90 V respectively was obtained for Cu₂O, CuSCN, CuI and spiro-OMeTAD at the thickness of 1 μm. It can be sated that the optimal thickness is crucial for maximizing the absorption of incident sunlight by the material, which in turn facilitates the generation of a higher number of electron-hole pairs. The perovskite absorbing layer, which is excessively thin may not fully absorb light, leading to a decrease in short-circuit current density and overall efficiency. On the other hand, a layer that is too thick can pose difficulties, including heightened bulk recombination, diminished carrier extraction efficiency, and increased resistive losses, all stemming from the restricted diffusion lengths of charge carriers³³.

Fig. 6

Influence of thickness of perovskite absorber on the performance of PSCs with different HTLs.

It is crucial to understand the operating temperature of PSCs under ambient atmospheric conditions. The device performance of PSCs varied under different environmental conditions. Here the operation temperature of the PSCs is varied from 250 K to 400 K to understand the behaviour of designed PSCs in the real-world. High temperature leads to change the carrier dynamics, enhance the electron-holes recombination and non-radiative recombination which leads to reduce the V_OC and FF³⁴. The operating temperature directly affects the V_OC and the rate of change of V_OC directly related to the operating temperature of the device as shown in the following equation:

$$\:\frac{\:\text{d}\:{V}_{oc}}{\:\text{d}\text{T}}=\frac{\:\:{V}_{oc}}{\:\text{T}}-\frac{\:\:{E}_{g/q}}{\:\text{T}}=0$$

(13)

As shown in Fig. 7(a-d), the PCE, V_OC (V) of the device decreases with increase in operating temperature, however, FF decreases with increase in the temperature. Slight decrement is observed in the J_SC with increase in the temperature as shown in Fig. 8(a-d). The maximum PCE of 7.14%, 5.84%, 5.15% and 4.54%; J_SC of 8.74 mA/cm², 8. 56 mA/cm², 8.49 mA/cm² and 9.46 mA/cm²; FF of 61.29%, 59.62%, 58.04% and 56.95% and V_OC of 1.33 V, 1.14 V, 1.04 V and 0.95 V respectively was obtained for Cu₂O, CuSCN, CuI and spiro-OMeTAD at 220 K operating temperature. With increase in operating temperature the thermal energy increases within perovskite absorber which further enhance the ion migration and therefore it leads to hysteresis and instability in the device³⁵. The superior PCE of PSCs obtained at 250 K exhibited the stability of the device under low light conditions.

Fig. 7

The variation in PCE and FF of PSCs with change in temperature using different HTLs (a) CuI, (b) CuSCN, (c) Cu₂O and (d) Spiro-OMeTAD.

Fig. 8

The variation in V_OC and J_SC of PSCs with change in temperature using different HTLs (a) CuI, (b) CuSCN, (c) Cu₂O and (d) Spiro-OMeTAD.

Series resistance (R_S) is a significant factor influencing the overall performance of PSCs. While it has a minor impact on the J_SC, it directly influences the FF and efficiency of PSCs, leading to a decrease in overall device efficiency³⁶. An increase in R_S results in a reduction in carrier density, which subsequently causes a decline in the current generated by the device. The value of R_S is adjusted, as shown in Fig. 9 (a-d), within the range of 0 to 12 Ω·cm² to evaluate the performance of the device under these conditions. It has been observed that the variation in series resistance do not affect the V_OC and slight reduction in J_SC value. However, significant reduction in FF and PCE for all HTLs based PSCs. The device efficiency of Cu₂O, CuSCN, CuI and spiro-OMeTAD is varied from 7.60 to 7.30%, 6.28-6.00%, 5.56–5.30%, and 5.68–5.41% respectively with variation in series resistance from 0 to 12 Ω·cm². The reduction of R_S value by enhancing material conductivity, refining interface engineering, and improving device architecture is essential for attaining high-performance perovskite solar cells. The final device output of PSCs with different HTLs (CuI, CuSCN, Cu₂O, Spiro-OMeTAD) is shown in Table 5.

Fig. 9

Effect of change in series resistance (R_S) on device performance of PSCs with different HTLs.

Table 5 Final device output of PSCs with different HTLs (CuI, CuSCN, Cu₂O, Spiro-OMeTAD).

Afterwards, optimization study of various parameters is performed along with capacitance-voltage (C-V), conductance-voltage (G-V), capacitance-frequency (c-f), conductance-frequency (G-f), Nyquist and bode plot are studied to identify the possibilities to enhance the optoelectronic properties of PSCs and investigate the charge transport mechanisms, defect-assisted recombination in the device. The C-V and C-f curves serve as critical parameter for investigation of the electrical characteristics and dynamic responses of PSCs. The C-f analysis is used for detecting trap states, evaluating dielectric properties, and understanding charge accumulation effects, where a decrease in capacitance with frequency indicates the presence of deep trap levels. The G-f measurement scales light on recombination losses and interface defects, as an increase in conductance at specific frequencies points to defect-assisted charge transport. The C-V profiling is crucial for determining built-in potential, depletion width, and doping concentration, all of which are vital for enhancing charge transport layers. Additionally, the G-V measurements facilitate the evaluation of interface recombination and contact resistance by examining conductance changes in response to applied voltage. Together, these techniques provide a systematic understanding of charge carrier behaviour, defect states, and interface quality, contributing to the optimization of PSC efficiency^37,38,39. Here C-V and G-V measurements are performed within the range of −1.5 V to 1.5 V for different HTL materials to understand the charge carrier dynamics. The depletion and diffusion capacitances are associated with p-n junctions. When a reverse bias is applied, the depletion capacitance exceeds the diffusion capacitance because of the expansion of the depletion region. In contrast, when forward bias is applied, the diffusion capacitance becomes dominant as charge carriers are injected, resulting in an increase in capacitance. It can be observed from Fig. 10(a) that the value of capacitance shows almost constant behaviour up to 0.6 V and V_peak shift is observed in different PSCs. The PSCs with Cu₂O HTL experienced higher peak compared to other HTL based PSCs. The lower offset value corresponds due to the less charge accumulation that resulted into high carrier mobility. The PSC with Cu₂O HTL obtained the maximum capacitance of 5.24nF/cm² at 1.01 V. The G-V curve offers valuable information regarding charge transport mechanisms, defect-assisted recombination, and the integrity of the interfaces among the layers within the perovskite solar cell structure. Figure 10(b) illustrates the G-V curve with different HTLs in the voltage range of −1.5 to 1.5 V. It can be observed that the conductance is nearly constant and show stable behaviour for different HTLs based PSCs up to nearly 0.1 V. Beyond this value the sharpe increment is observe in spiro-OMeTAD based PSCs after 0.23 V and shows the maximum value of G up to 0.07 S/cm². However, Cu₂O HTL based PSCs shows constant value of G up to 0.64 V and afterwards sharp increment behaviour is observed and maximum value reached up to 0.006 S/cm². The maximum conductance value of CuI and CuSCN based PSCs lies between 0.07–0.06 S/cm². The value of conductance increases when defects or trap state become predominant and therefore providing the information about density and energy level of theses traps. In Cu₂O based PSCs the trap state is less active compared to CuSCN, CuI and Spiro-OMeTAD based PSCs and hence showing superior device performance.

Fig. 10

Capacitance-voltage (C-V), and Conductance-Voltage (G-V) curve of PSCs.

The C-f and G-f curve allow to understand the charge transport mechanisms, trap states, and ionic migration by assessing capacitance across a wide range of frequencies. At lower frequencies, the C-f curve is particularly responsive to ionic migration and defect-related effects, whereas at higher frequencies, it indicates the bulk dielectric characteristics and the dynamics of charge recombination^40,41,42. Figure 11 (a-b) shows the C-f and G-f curve over the frequency range of 100 Hz to 1 MHz. At lower frequency the spiro-OMeTAD, CuI, CuSCN, Cu₂O based PSCs shows the capacitance value of 5.18nF/cm², 5.15nF/cm², 5.16nF/cm², and 5.13nF/cm² respectively as shown in Fig. 11(a). After 1 × 10⁵ HZ C-f curve with different HTL based PSCs follow similar type of decrement trend up to frequency of 1Mz. The lower frequency range in the C-f curve attributed to the defects and it can be stated that spiro-OMeTAD HTL based PSCs with lead-free Cs₂AgBiBr₆ absorber undergoes defect related effects and ionic migration problem. In contract, lower capacitance value of Cu₂O HTL based PSCs has been observed compared to other HTL based device with Cs₂AgBiBr₆ absorber. This is due to appropriate band alignment between Cu₂O with Cs₂AgBiBr₆ perovskite absorber which reduces defects at interfacial points. The G-f characteristics of PSCs with different HTL is shown in Fig. 10 (b).

Fig. 11

Capacitance-frequency (C-f), and Conductance- frequency (G-f) curve of PSCs.

Further impedance measurement study was performed for PSCs with different HTLs to investigate the status of charge carrier recombination in the device. The Nyquist plots are shown in Fig. 12, represent the semicircle with different diameter. Typically, Nyquist plots in PSCs exhibit two semi-circles that represent various physical phenomena within the device⁴². The initial semicircle, seen at elevated frequencies, relates to charge transport and transfer at the interfaces, especially at the Au (gold) back electrode or other conductive connections. This high-frequency behaviour illustrates the resistance and capacitance of charge carriers as they traverse the contact layers and interfaces. In contrast, the second semicircle, which establishes at lower frequencies, signifies carrier recombination processes taking place within the device, predominantly at the interfaces among the ETL, the perovskite absorber layer, and the HTL. Here second case is observed, and it has found that Cu₂O HTL based PSCs having larger diameter of semicircle and spiro-OMeTAD based PSCs represent lower diameter of semicircle. The diameter of semicircle represents recombination resistance of the device. The higher value of recombination resistance exhibits lower charge carrier recombination and therefore reduced the series resistance of the device⁴³. The Cu₂O HTL based PSCs faces lower series resistance in the device resulting into improved device efficiency.

Fig. 12

Nyquist plot of PSCs with different HTLs.

Figure 13 illustrate the bode plot containing impedance magnitude and phase angle of the PSCs with different ETLs. In Fig. 13 (a), the PSC with Cu₂O ETL exhibited high value impedance of 2.13 × 10³ Ω.cm² whereas the impedance of PSCs with different HTLs are 1.73 × 10³ Ω.cm², 1.52 × 10³ Ω.cm², 1.32 × 10³ Ω.cm² for CuSCN, CuI and spiro-OMeTAD. The magnitude of impedance is inversely correlated with the recombination processes occurring within the device^44,45. The increased rates of recombination in PSCs lead to a decrease in recombination resistance, which resulted into improved PCE. Figure 13 (b) represent the variation in phase angle with different HTL. Based up on the angular phase and frequency plot an incomplete peak is observed in the high-frequency range, which is recognized to the capacitance of the depletion layer within the device. In contrast, the low-frequency region is associated with the influence of the double layer capacitance. The phase angle of PSCs decreases with increase in the frequency and shift towards higher frequency. The above discussion indicted the Cu₂O as suitable hole transport material for lead-free Cs₂AgBiBr₆ based PSCs.

Fig. 13

Bode plot of PSCs with different HTLs.

At last, Fig. 14 presents the relationship between current density (mA/cm²) and voltage (V) as well as the quantum efficiency (%QE) in relation to wavelength (nm) for the final optimized devices, which have been refined based on all the most favourable proposed parameters.

Fig. 14

I-V curve and QE characterises (inset) of PSCs with Cu₂O HTL.

The essential optimization techniques for device fabrication, suggested by SCAPS device simulation, include the optimization of layer thicknesses, alignment of energy levels, defect densities and operating temperature to enhance PCE. SCAPS advances in determining the optimized thickness for the perovskite absorber and different HTL, facilitating effective light absorption and carrier extraction. Additionally, it enables the modification of band alignment at interfaces to reduce recombination losses and enhance charge selectivity. These simulation-based understandings assist researchers in choosing appropriate materials, deposition methods, and interface engineering strategies to develop high-performance, stable devices.

Conclusion

In conclusion, lead-free PSCs were designed in SCAPS simulation software using cell configuration of FTO/TiO₂/Cs₂AgBiBr₆/HTLs/Au. Initially, the designed model was successfully verified, and it is in a good agreement with the reported results. The simulation study performed here follows a systematic methodology, wherein each device parameter is changed independently to assess its effect on device performance and to obtain a deeper understanding of the primary reasons for its impact. Nevertheless, the simulation fails to consider environmental elements like moisture, oxygen, and thermal influences, all of which play a crucial role in the long-term stability of actual devices. Initially, numerical simulation was conducted by optimizing different parameters such as defect density and thickness of perovskite absorber, operating temperature and series resistance of the PSCs. Afterwards, C-V, G-V, C-f and G-f studies were performed to evaluate the charge transport mechanisms, trap states, and ionic migration. The Cu₂O HTL based PSCs experienced lower defects at interfacial point due to suitable band alignment with Cs₂AgBiBr₆ perovskite absorber. The PSCs exhibited maximum device efficiency of 7.60%, 6.28%, 5.56%, and 5.68% for Cu₂O, CuSCN, CuI and spiro-OMeTAD based PSCs. This simulation study thus presents new opportunities for the development of lead-free, stable all-inorganic PSCs.