Optimizing Cs₂CuBiBr₆ double halide perovskite for solar applications: the role of electron transport layers in SCAPS-1D simulations

Abstract

Perovskite solar cells are commonly employed in photovoltaic systems because of their special characteristics. Perovskite solar cells remain efficient, but lead-based absorbers are dangerous, restricting their manufacture. Therefore, studies in the field of perovskite materials are now focusing on investigating lead-free perovskites. The SCAPS-1D simulator is used to simulate the impact of lead-free double perovskite as the absorber in perovskite solar cells. The research examines how the effectiveness of solar cells is impacted by a hole transport layer (CBTS) and several electron transports layers (WS₂, C₆₀, PCBM, and TiO₂), using Ni and Al acting as the back and front contacts metal. This work explores the impact of a Cs₂CuBiBr₆ perovskite as a solar cell absorber. The effectiveness of these device structures depends on defect density, absorber thickness, ETL thickness, and ETL combination. With WS₂, C₆₀, PCBM, and TiO₂, the device's power conversion efficiency (PCE) is 19.70%, 18.69%, 19.52%, and 19.65%, respectively. This research also highlights the impact of the absorber and HTL thickness. This investigation further included the analysis of the valence band offset (VBO) and conduction band offset (CBO). We also investigated the current density–voltage (J–V), quantum efficiency (QE), series and shunt resistance, capacitance-Mott–Schottky characteristics, and photocarrier generation–recombination rates and effective temperature. This study provides crucial structural design guidelines for a lead-free double perovskite device and highlights solar energy optoelectronic developments.

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1. Introduction

With the potential to significantly influence human society and mold the future of renewable energy, solar cells represent a promising technological advancement. Sustainable energy is a plentiful resource that emits no carbon dioxide, is free to use, and is freely available.^1,2 Photovoltaic cells use visible light to generate power by converting solar photons to electric energy.^3,4 In the last two decades, significant technological advancements in photovoltaic technology have driven substantial cost reductions and remarkable improvements in the PCE of PV cells. The exploration and application of innovative materials present exciting possibilities for even greater advancements in the years to come.^5,6 There are three generations of photovoltaic cell technology. In 1954, Bell Laboratories produced the first generation, with an efficiency of 6%. Second-generation solar cells, also called thin-film photovoltaic cells, offer a more affordable option than conventional silicon wafer-based cells. These thin-film cells have clear benefits in terms of material efficiency and lower total mass. They are distinguished by their flexibility and lightweight construction.^3,7 Third-generation solar cells have improved dependability and efficiency compared to previous versions. The exceptional efficiency of these cells is due to their diversified composition, particularly including conductive polymers, organic dyes, silicon nanowires, and nanomaterials with large band gaps.^8–10

The SCAPS-1D simulator has been utilized by researchers for numerical simulations, utilizing computational analysis to support cost-effective production processes and optimize solar cell design. Before a device is put into production, it can be thoroughly evaluated in a virtual environment using simulation tools, which can save a lot of resources and time.¹¹ The SCAPS 1D simulation program facilitates the exploration and linkage of experimental as well as theoretical studies. Previously, planar FA-based PSCs were analyzed and their performance was illustrated using both numerical simulations and experimental analysis.¹² More than ever, the necessity of alternative energy sources is highlighted by the world's expanding energy demand, the increasing exhaustion of fossil fuel resources, and the rising levels of pollution that feed global warming.^13–15 Renewable energy is becoming increasingly acknowledged as a vital source of electricity because of the worldwide problem of global warming. Especially remarkable is solar power, which is the most abundant energy resource on the planet. The high initial prices and low conversion efficiency of solar power generation remain barriers to mainstream adoption. It is anticipated that advancements in perovskite-based solar cell structure will increase production capacity while lowering resource and energy consumption.^16,17 The key factors driving perovskite film photovoltaics' growing popularity are their ability to produce them quickly and effectively, as well as the low material requirements and resulting cost reductions.^6,18–20

The perovskite material, such as lead-free double perovskite structure Cs₂B′B′′Br₆ where B′ = Cu and B′′ = Bi. This perovskite structure is a lead-free non-toxic substance with preferred absorption.²¹ Increased charge carrier production, a higher rate of photon generation, resulting in reduced energy loss and an enhanced concentration of electric charge carriers at the electrodes.^22,23 In comparison to conventional bismuth-based double perovskite solar cells, Cesium Copper Bismuth Bromide (Cs₂CuBiBr₆), referred to as the absorber, demonstrates enhanced thermal stability, owing to its single crystal structure and lower susceptibility to moisture. When compared to CH₃NH₃PbX₃, McClure and coworkers observed that Cs₂AgBiBr₆ and Cs₂AgBiCl₆ had a superior bandgap and good stability.²⁴ Cs₂AgBiBr₆ and Cs₂AgBiCl₆ exhibit poor efficiency due to high charge carrier effective masses, insufficient charge carrier transport properties, and large band gaps (>2 eV),^25–27 making them unsuitable for solar cell applications. Conversely, compared to Cs₂AgBiBr₆ and Cs₂AgBiCl₆, the Cs₂CuBiBr₆ absorber demonstrated an ideal band gap (1.24 eV), larger light absorption abilities, and superior performance, making it appropriate for the PSC.^21,28,29 Due to its substantial bandgap, which is closely correlated with V_OC, the inclusion of bromide in the perovskite might facilitate a high V_OC. In addition to the preferred optical band gap and light spectrum, their strength under illumination in humid conditions, and elevated temperatures are markedly enhanced in comparison to organic lead halide perovskites.³⁰ In PSCs, utilizing an appropriate electron transport layer (ETL) and a hole transport layer (HTL) can improve the absorber's performance and efficiency. A light-absorbing perovskite layer is often positioned between the ETL and the HTL in mesoporous and planar structures, which are common in solar cell systems. Electrons can move between mesoscopic perovskite structures and nanoparticles of mesoporous metal oxides like TiO₂ (ref. 31 and 32) and ZnO³³ through the ETL, while holes can successfully transmit through HTLs.³⁴ The thickness of the ETL, HTL, absorber layer, as well as their interface and phase matching characteristics, are the main determinants of photovoltaic parameters such as the open-circuit voltage (V_OC), short-circuit current density (J_SC), fill factor (FF), and power conversion efficiency (PCE). Several semiconductor materials have been used as ETLs, including ZnO, TiO₂, WO₃, I₂O₃, WS₂, PCBM, C₆₀, Al₂O₃, and SnO₂.^35–38 Prior research has not extensively investigated the usage of ETLs like WS₂, PCBM, and CdS in combination with Cs₂CuBiBr₆ perovskite-based solar cells.²¹ The ETL used in this work comprises Tungsten Disulfide (WS₂), Buckminsterfullerene (C₆₀), phenyl-C₆₁ butyric acid methyl ester (PCBM), and Titanium Dioxide (TiO₂) as the electron transport materials. The electron transport layer made of tungsten disulfide (WS₂) is very desirable in optoelectronics because of its adaptability and excellent bandgap.^39,40 Furthermore, the effective extraction of electrons has been observed by organic electron transport layers, such as C₆₀, when combined with the perovskite layers.⁴¹ The need for high-temperature heating of TiO₂ to attain the rutile form for solar application, along with the confined movement of electrons, impedes its effectiveness as an electron transport material in PSCs.^31,42–44 The PCBM ETL obviates the necessity for thermal annealing or processing at high temperatures, therefore considerably streamlining the production procedure and reducing production costs.

Moreover, the HTL and nearby surfaces affect the solar cell's efficiency, durability, and manufacturing cost.^45,46 Solar cell performance is improved by small-molecule HTLs; however, they don't have enough photostability and thermal stability. By comparison, polymeric HTLs are attractive because they are suitable with other materials, water-repellent, and can withstand high temperatures.⁴⁷ But these HTLs could have limitations with their optoelectronic characteristics, which might lead to lower efficiency. Due to the increasing demand for affordable solar cell manufacturing, earth-abundant, air-stable thin-film materials like copper barium thiocyanate (CBTS) are being investigated as possible substitutes for widely used HTLs like Cu₂O, CuSCN, CuSbS₂, NiO, P3HT, PEDOT: PSS, spiro-OMeTAD, CuI, CuO, and V₂O₅. CBTS is an appropriate option for HTL application due to its large atomic size, non-centrosymmetric crystal structure, high absorption coefficient, variable bandgap, and effective light-absorbing properties.^47–50 The shallow valence band of CBTS aligns well with Cs₂B′B′′Br₆, leading to modest energy loss when CBTS is used as the hole transport layer in Cs₂B′B′′Br₆ (where B′ = Cu and B′′ = Bi) based PSCs. Prior research has shown that the CBTS HTL had favorable characteristics due to its suitable absorption coefficient and electron affinity.⁵¹

Therefore, ETL and HTL are implemented to improve the PV parameters of solar cells. Furthermore, this investigation on Cs₂CuBiBr₆ has shown substantial advancement, increasing efficiency from the previous 14.08% to an improved 19.70%. The energy band alignment was likely enhanced by the use of CBTS as a hole transport layer (HTL) and Ni as the back-contact metal, which decreased energy losses during charge carrier transport. This ideal alignment improves charge extraction and minimizes recombination. The use of ITO instead of FTO may have enhanced optical transmittance and electrical conductivity. Thus, more photons are able to reach the active perovskite layer, which improves the production of charge carriers. These results highlight the significant advancements attained in our study, which boost the performance of the examined absorber materials. Utilizing SCAPS-1D software to investigate single absorber-based perovskite solar cells enhances experimental efficiency by virtually adjusting device settings. SCAPS-1D determines optimal designs and material selections by simulating many combinations, thus assisting experimentalists in the fabrication of high-performance devices.

This process expedites development, ensuring more efficient and accurate manufacturing procedures, eventually resulting in improved device performance. Therefore, this investigation entails the assessment of Cs₂CuBiBr₆ in a variety of configurations, such as WS₂, C₆₀, PCBM, and TiO₂ as electron transport layers (ETL), CBTS as hole transport layers (HTL), Al as the front contact metal, and Ni as the back-contact metal. The photovoltaic (PV) performance is investigated and evaluated by observing the impact of variations in the absorber thickness and ETL thickness, as well as the impact of series and shunt resistance on PV parameters, to determine the optimal configurations. To further understand the studied SC designs, we also compute the current–voltage (J–V) curves, capacitance–voltage (C–V) properties, quantum efficiency (QE), generation and recombination rate.

2. Device concept modeling and design

2.1. Numerical simulation employing SCAPS-1D

Understanding the basic principles of solar cells and determining the major variables affecting their efficiency is feasible through the computational model's framework. The SCAPS-1D application may be used to numerically solve significant 1D semiconductor problems.^52–55 Eqn (1) indicates that the charges are related to the electrostatic potential according to Poisson's equation.⁵⁶

The above equation represents the electronic potential (ψ), relative permittivity (ε_r), free space permittivity (ε₀), ionized acceptor densities and donor densities (N_A and N_d), electron and hole densities (n and p), electron and hole distributions (ρ_p and ρ_n), and electronic charge (q). When generation, recombination, drift, and diffusion are all evaluated at the same time, the continuity equation emerges as the governing equation. The continuity equations for the variation in electron and hole concentrations are presented in eqn (2) and (3).

In this scenario, J_n and J_P represent the current densities of electrons and holes, G_n and G_P represent electron and hole generation, and R_n and R_P represent electron and hole recombination. The charge carrier drift-diffusion equations used to compute the electron and hole current densities in solar cells are given by eqn (4) and (5).

J_n = qμ_nnε + qD_n∂n (4)

J_P = qμ_Ppε + qD_P∂p (5)

Here, carrier mobility is indicated by μ_n and μ_P, whereas electron and hole diffusion coefficients are indicated by D_n and D_P. The coefficient of diffusion is dependent on the mobility and durability of the carrier, based on the Einstein relationship.⁵⁷ The film absorption constant was obtained using the newly modified E_g-sqrt model, an updated version of the conventional sqrt (hν − E_g) model. The “Tauc law” define this relationship as seen in eqn (6).where hν denotes photon energy, bandgap, and absorption coefficient are represented by E_g. Eqn (7) and (8) establish a relationship between the model constants α₀ and β₀ and the standard model constants A and B, as shown below:

Under steady-state factors, SCAPS-1D determines the basis of semiconductor equations. Fig. 1 describes the simulation technique of SCAPS-1D. The program was started to execute the SCAPS-1D simulation, and the solar cell's construction consisted of several layers such as WS₂, C₆₀, PCBM, and TiO₂ acting as ETL and Cs₂CuBiBr₆ acting as the absorber of perovskite. Inputs included material properties such as electron affinity, dielectric constant, carrier mobilities, bandgap, etc., and operating characteristics such as temperature, AM1.5 G illumination intensity, bias voltage range for J–V characteristics, etc. Capacitance, quantum efficiency (QE), J–V properties, Mott–Schottky characteristics were among the several measures that were considered. Next, we solved Poisson's equation, continuity equations, and drift-diffusion equations before initiating the simulation. We examined the results using graphical tools, such as origin, to evaluate the efficiency of solar cells.

Fig. 1 SCAPS-1D operational instruction.

2.2. Device structure

The main device's conceptual design is shown in Fig. 2a. The formation of the configuration of a lead-free double perovskite halide solar cell is accomplished by the combination of ETL, HTL, and back contact with the Cs₂CuBiBr₆ absorber layer. As a solar cell, the Cs₂CuBiBr₆ absorber has an n–i–p configuration. In this case, an n–i–p structure outperforms a standard semiconductor p–n junction due to its superior long-wavelength sensitivity. The depletion zone of an n–i–p structure is positioned deep inside the device, including the intrinsic area. Photons penetrate deeply into cells when they are subjected to long wavelengths. Despite this, the creation of electron–hole pairs within and outside the zone of depletion is the only source of current. An increase in depletion width allows for more effective production and distinction of electron–hole pairs, which ultimately turn increases the cell's quantum efficiency.⁵¹ The photon-capturing properties of Cs₂CuBiBr₆ are a result of its double heterostructure, which guarantees charge and photon confinement and functions as an ohmic contact around the heavily doped ETL and HTL. When designing this device, we keep the following elements in consideration: CBTS for the HTL, Ni for the back-metal contact, Al for the front-metal contact, WS₂, C₆₀, PCBM, and TiO₂ for the ETLs, and cesium copper bismuth bromide for the absorber layer. Fig. 2a depicts the structure of the ITO/ETL/Cs₂CuBiBr₆/CBTS/Ni device. The simulated input parameters for the absorber layer, ETLs, along with HTL, are presented in Table 1, along with the input parameters for the interfacial defect layers included in Table 2. While we execute the SCAPS-1D investigation, the software helps us analyze the performance of different double PSC configurations. The formation of double perovskite structures is achieved by maintaining an ambient temperature of 300 K, a frequency of 1 MHz, and an AM1.5G spectrum.

Fig. 2 The Cs₂CuBiBr₆ absorber's (a) crystal arrangement and (b) energy band aligning associated with various ETL materials (WS₂, C₆₀, PCBM, and TiO₂).

Table 1 Parameters applied in this research involve the absorber layer, HTL, ETL, and ITO

Parameter (unit)	ITO	ETL				Cs2CuBiBr6	HTL
		WS2	C60	PCBM	TiO2		CBTS
Ref.	51 and 58	21 and 51	51 and 59	21 and 59	51 and 60	21	48 and 51
Thickness [μm]	0.5	0.1	0.05	0.05	0.03	0.6	0.100
Bandgap, Eg [eV]	3.5	1.8	1.7	2	3.2	1.24	1.90
Electron affinity, X [eV]	4	3.95	3.9	3.9	4	3.95	3.60
Dielectric permittivity, εr (relative)	9	13.6	4.2	3.9	9	5.40	5.40
CB effective density of states, NC [cm^−3]	2.2 × 10^18	1 × 10^18	8.0 × 10^19	2.5 × 10^21	2 × 10^18	1.46 × 10^19	2.2 × 10^18
VB effective density of states NV [cm^−3]	1.8 × 10^19	2.4 × 10^19	8.0 × 10^19	2.5 × 10^21	1.8 × 10^19	3.34 × 10^19	1.8 × 10^19
Electron thermal velocity [cm^−1 s]	1 × 10^7	1 × 10^7	1 × 10^7	1 × 10^7	1 × 10^7	1.39 × 10^7	1 × 10^7
Hole thermal velocity [cm^−1 s]	1 × 10^7	1 × 10^7	1 × 10^7	1 × 10^7	1 × 10^7	1.06 × 10^7	1 × 10^7
Electron mobility, μn [cm^2 V^−1 s^−1]	20	100	8.0 × 10^−2	0.2	20	13.98	30
Hole mobility, μh [cm^2 V^−1 s^−1]	10	100	3.5 × 10^−3	0.2	10	2.98	10
Shallow uniform donor density, ND [cm^−3]	1 × 10^21	1 × 10^18	1 × 10^17	2.93 × 10^17	9 × 10^16	1 × 10^15	0
Shallow uniform acceptor density, NA [cm^−3]	0	0	0	0	0	1 × 10^15	1 × 10^18
Defect density, Nt [cm^−3]	1 × 10^15a	1 × 10^15	1 × 10^15	1 × 10^15	1 × 10^15	1 × 10^15a	1 × 10^15
Capture cross-section for electrons [cm^2]	1 × 10^−15	1 × 10^−15	1 × 10^−15	1 × 10^−15	1 × 10^−15	1 × 10^−15	1 × 10^−15
Capture cross-section for holes [cm^2]	1 × 10^−15	1 × 10^−15	1 × 10^−15	1 × 10^−15	1 × 10^−15	1 × 10^−15	1 × 10^−15

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Table 2 This perovskite solar cell for Cs₂CuBiBr₆ uses interface parameters

Interface	Defect type	Capture cross-section: electrons/holes [cm^2]	Distribution of energy	Reference for defect energy levels, Et	Interface defect density [cm^−2]
ETL/Cs2CuBiBr6	Neutral	1 × 10^−17	Single	Above the VB maximum	1 × 10^10
		1 × 10^−18
Cs2CuBiBr6/CBTS	Neutral	1 × 10^−18	Single	Above the VB maximum	1 × 10^10
		1 × 10^−19

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2.3. Band orientation of Cs₂CuBiBr₆ utilizing absorber with various ETLs

The band orientation of several heterostructures based on the Cs₂CuBiBr₆ absorber is shown in Fig. 2b. It shows the valence band maxima (E_V), conduction band minima (E_C), and the quasi-Fermi levels of electrons (F_n) and holes (F_p). While F_n and E_C continue to exhibit a harmonic connection, F_p aligns with E_V in different kinds of ETL. F_n and E_V stay at equal levels across all ETLs using CBTS as the HTL; therefore, F_n intersects E_C and inhibits the flow of holes and electrons from ETLs and HTL. A nickel (Ni) back contact with a work function (WF) of 5.5 eV effectively captures holes from the HTL, while aluminum (Al) front contact, having a work function (WF) of 4.1 eV efficiently collects electrons.

3. Result and discussion

3.1. Impacts of conduction band offset (CBO) and valence band offset (VBO)

The ETL and HTL are required for efficiently moving photo-generated charge carriers from the absorber to their specific contacts in perovskite solar cells. Furthermore, they restrict the recombination of charges at the ETL/absorber and absorber/HTL interfaces by delaying the movement of electrons and holes toward specific charge carrier accumulation at each electrode.⁶¹ When sunlight strikes the solar cell, the perovskite absorber produces electrons and holes. Subsequently, these charge carriers are split up and distributed to the relevant contacts for collection. The effectiveness of the splitting process depends on the conduction band offset (CBO) and valence band offset (VBO) at the ETL/absorber and absorber/HTL interfaces, respectively. The performance of the device is directly affected by these offsets. At the ETL/absorber interface and absorber/HTL interface, there are three distinct kinds of barriers: cliff-like, nearly flat, and spike-like.⁶² The energy differential in cliff-like barrier facilitates the movement of carriers, owing to the band bending at the interfacial layers. In particular, when interface defects are present, band bending in a cliff-like barrier accelerates recombination at the interface, which reduces the V_OC and lowers the solar cell's efficiency. The energy difference is zero, and there is no band offset in a nearly flat barrier. Here, the interfaces of CBO and VBO are almost flat, and the produced electrons and holes may move freely due to the absence of an energy barrier. When the spike-like barrier is present, the energy differential, caused by the shape of band bending at the layer interface, prevents transporting carriers from moving through the structure. Spike-like band bending reduces recombination at the interface, especially between absorber valence band holes (conduction band electrons) and ETL conduction band electrons (HTL valence band holes).^63–66

The CBO at the ETL/absorber interface is defined as

CBO = X_absorber − X_ETL (9)

While X_ETL exceeds X_absorber, a negative CBO for a cliff-like barrier indicates that the ETL's conduction band minimum (CBM) is smaller compared to the absorber's. If the value of CBO is zero, then the barrier is nearly flat. Conversely, the barrier of spike-like, having a positive CBO, is seen when the CBM of the ETL is greater than the CBM of the absorber (X_ETL < X_absorber).

Conversely, the VBO at the absorber/HTL interface is defined as⁶¹

VBO = X_HTL − X_absorber + E_g,HTL − E_g,absorber (10)

VBO is depicted as Valence Band Offsets, X_HTL represents the electron affinity of the HTL, while E_g,absorber and E_g,HTL denote the bandgaps of the absorber and HTL, consequently.

The absorber/HTL interface and the ETL/absorber interface both exhibit similar barrier types. The absorber exhibits a cliff-like barrier having a negative VBO when its valence band maximum is less than the HTL's. When the VBO is zero and the barrier is nearly flat, there is no band offset. On the other hand, the barrier of spike-like occurs when the HTL's valence band maximum is less than the absorber's and may be identified by a positive VBO.

Eqn (9) and (10) were used to determine the CBO and VBO.⁶¹ For WS₂ the conduction band offset (CBO) and valence band offset (VBO) are given below.

The CBO at the interface between the absorber and ETL is = X_absorber − X_ETL = 3.95 − 3.95 = 0 eV.

This indicates that the CBO is at zero, and the barrier is nearly flat.

The VBO at the HTL and the absorber interface is = X_HTL − X_absorber + E_g,HTL − E_g,absorber = 3.6 − 3.95 + 1.9 − 1.24 = 0.31 eV.

The calculation shows that the VBO is positive, and the barrier is spike-like.

The values of CBO and VBO were determined using the same approach as for the remaining ETLs in Table 3. For the ETL C₆₀, both the CBO and VBO exhibit positive values, forming spike-like barriers. Similarly, in the case of the ETL PCBM, both CBO and VBO are positive and also form spike-like barriers. In contrast, the ETL TiO₂ presents a negative CBO, forming a cliff-like barrier, while the VBO remains positive, forming a spike-like barrier.

Table 3 Determined the value of VBO and CBO utilizing various ETLs

Absorber	ETLs	CBO	VBO
Cs2CuBiBr6	WS2	0	0.31
	C60	0.05	0.31
	PCBM	0.05	0.31
	TiO2	−0.05	0.31

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The higher V_OC in the CBTS device, featuring a spike-like barrier, is attributed to reduced recombination at the absorber/CBTS interface, thereby enhancing carrier collecting efficiency. Conversely, the cliff-like barrier in the spiro-OMeTAD device enhances hole transport but results in increased recombination, hence reducing V_OC.²¹ Therefore, despite the less effective hole transport, the spike-like barrier in CBTS reduces recombination, leading to a higher V_OC and overall superior device performance.

3.2. Band diagram

With the use of cesium copper bismuth bromide, the energy band diagrams of the PSCs that were utilized are shown in Fig. 3a–d. The offset between the valence and conduction bands, that indicates disparity in the valence band between the HTL and absorber layer, is affected through every ETL in this scenario, including an absorbing layer of Cs₂CuBiBr₆ as well as CBTS considering the HTL. The PSC's reliability and efficacy are highly influenced by the energy level alignment. In PSCs, photo-generated electrons are injected into the ETL's conduction band while holes are simultaneously transported to the HTL. The next step is collecting the electrons and holes from the front-contact metal (Al) and the back-contact metal (Ni), according to the sequence. If the energy levels (conduction band and valence band) of the materials interacting at an interface are not perfectly matched, a phenomenon known as energy band mismatch will occur. The device's performance characteristics have a major impact on the energy band mismatch at the Cs₂CuBiBr₆ and HTL as well as ETL and Cs₂CuBiBr₆ interfaces. To enable effective electron extraction, the ETL's conduction band minimum (CBM) should be either slightly lower than or closely aligned with the CBM of Cs₂CuBiBr₆. Likewise, to facilitate efficient hole transmission, the valence band maximum (VBM) of the HTL should be in near alignment with or somewhat higher than the VBM of Cs₂CuBiBr₆. Any large mismatch may result in energy barriers that reduce carrier transit and increase interfacial recombination, both of which reduce the efficiency of the device. Consequently, electronic property tuning of ETL and HTL materials becomes an essential task. To properly remove electrons at the interface ETL/Cs₂CuBiBr₆, the electron affinity of ETL should be greater than that of Cs₂CuBiBr₆. On the other hand, the HTL must have a lower ionization energy to extract holes at the interface Cs₂CuBiBr₆/HTL. Fig. 3 shows that in the four best configurations of Cs₂CuBiBr₆-based devices, the Fermi level moves inside the conduction band, which is close to it. In the Cs₂CuBiBr₆-based device, the Fermi level crossed the conduction band with WS₂ as the layer of ETL and CBTS as the layer of HTL (Fig. 3a). Fig. 3b–d illustrate the various architectures of devices based on Cs₂CuBiBr₆ perovskite. The degenerate semiconductor nature and pattern of C₆₀, PCBM, and TiO₂ as ETL and CBTS as HTL were similar to those illustrated in Fig. 3a. All four ETLs (WS₂, C₆₀, PCBM, TiO₂) provide identical results when used with the same heterostructure; this is because their bandgap energies are 1.8, 1.7, 2, and 3.2 eV, respectively. The energy of the valence band is almost equal to that of the quasi-Fermi levels F_n and F_p, as seen in Fig. 3a–d. F_p is always higher than E_V and F_n, and the conduction band (E_C) also shows synchronized behavior.

Fig. 3 Band diagram containing (a) WS₂, (b) C₆₀, (c) PCBM, and (d) TiO₂ for Cs₂CuBiBr₆.

3.3. Variation of absorber layer thickness and ETL layer thickness on PV performance for Cs₂CuBiBr₆

The ETL, positioned between the ITO and the absorber layer, may extremely influence the absorber layer's interaction with photons. To improve the PV output properties of the SCs, the thickness of the layer covering the absorber and the ETL is essential. The best-performing solar collectors need PV output tuning.⁶⁷ For this study, we considered WS₂, C₆₀, PCBM, and TiO₂ to be ETL, Cs₂CuBiBr₆ to be an absorber, and CBTS to be HTL. Fig. 4–7 show the contour maps of V_OC, J_SC, FF, and PCE for Cs₂CuBiBr₆ absorber-based PSCs, with performance varying with absorber thickness (0.4–1.2 μm) and ETL thickness (0.03–0.15 μm).

Fig. 4 Contour plots of V_OC resulting from the sequential change in absorber layer thickness and ETL layer thickness with ETLs including (a) WS₂, (b) C₆₀, (c) PCBM, and (d) TiO₂.

Fig. 4a illustrates that the maximum V_OC levels were observed when the absorber layer thickness was adjusted from 0.4 to 0.45 μm, while the thickness of ETL ranged from 0.03 to 0.15 μm. When the ETL layer thickness increases, the absorber layer thickness remains constant, but V_OC may decrease if the absorber layer is increased (Fig. 4a). The thickness of absorber layer remains constant for the C₆₀, PCBM, and TiO₂ structures, regardless of the increase in the ETL layer thickness (Fig. 4b–d). No matter how thick the ETL is, the WS₂, PCBM, and TiO₂ structures attained the greatest value of V_OC values considering the thickness of absorber layers are about 0.4 μm and 0.045 μm thick, respectively (Fig. 4a, c and d). Regarding the C₆₀ ETL-based structure, the maximum V_OC is found while the thickness of absorber is generally 0.4 to 0.45 μm and the thickness of the ETL is around 0.07 μm (Fig. 4b). Overall, most of the solar systems that were considered might have fewer V_OC with increasing absorber layer, as shown in Fig. 4. An increase in saturation current exceeding the photocurrent in the presence of a thick absorber layer can explain this phenomenon by increasing the carrier recombination rate.⁶⁸

In Fig. 5, we observe how the J_SC parameters of four different perovskite solar cells are affected by using different ETL and absorber layer thicknesses. The maximum J_SC values (36.77–37.24 mA cm⁻²) for WS₂-based solar cells are noted when the thickness of absorber is between 0.89 and 1.2 μm and the thickness of ETL is between 0.03 and 0.15 μm (Fig. 5a). Based on absorber thicknesses of 0.89–1.2 μm, the PCBM and TiO₂ ETL-based solar cells exhibit the same pattern, with peak J_SC values of 36.77–37.25 mA cm⁻² and 36.77–37.26 mA cm⁻², respectively (Fig. 5c and d). Increasing the absorber thickness while maintaining the ETL thickness results in higher J_SC values. If the absorber layer is thicker, higher light absorption, providing a higher generation rate and J_SC values. To minimize the effects of series resistance, thinner ETL layers may raise the current by decreasing the amount of recombination between electron–hole pairs. Keeping the ETL thickness at a minimum is recommended to enhance J_SC, V_OC, and overall efficiency. This will help minimize the production of large pinholes and rough surfaces. For WS₂, PCBM, and TiO₂ ETL-based solar cells, the appropriate absorber thickness is usually determined to be between 0.89 and 1.2 μm, and the ETL thickness does not affect J_SC fluctuation (Fig. 5a, c and d). Finally, Fig. 5b shows that the C₆₀-based ETL solar cells have the greater J_SC value (35.61–36.85 mA cm⁻²) when the absorber thickness is between 0.68 and 1.2 μm and the ETL thickness is between 0.03 and 0.05 μm. The observation shows that a smaller ETL and a thicker absorber may result in a higher J_SC for C₆₀. Increasing the generation rate and greater J_SC is possible with a larger absorber layer since it improves light absorption.⁶⁸ The impact of series resistance may be alleviated by a thin electron transport layer (ETL), which enhances current by diminishing the chance of recombination of electron–hole pairs. Crucially for J_SC, reducing the ETL thickness mitigates the development of bigger pinhole and uneven surface.⁶⁸

Fig. 5 Contour plots of J_SC resulting from the sequential change in absorber layer thickness and ETL layer thickness with ETLs including (a) WS₂, (b) C₆₀, (c) PCBM, and (d) TiO₂.

Fig. 6 depicts the change of the fill factor (FF) for perovskite solar cells following variations in the absorber and ETL thickness. For Cs₂CuBiBr₆-based PSCs, the WS₂ ETL had an FF of 78.98% when the thickness of absorber layer was between 0.4 and 0.5 μm and the ETL thickness was between 0.03 and 0.15 μm, shown in Fig. 6a. When the thickness of absorber varies from 0.4 to 0.5 μm and the thickness of ETL varies from 0.03 to 0.15 μm, the FF value is observed in solar cells connected to ETLs C₆₀, PCBM, and TiO₂-related solar cells, as shown in Fig. 6b–d. This pattern is almost identical to the one that we have found. With the increase in thickness of the absorber layer, the value of FF decreases, and it is not affected by the change in the thickness of the ETL. Alteration to the ETL's thickness may lead to a relationship between rising series resistance and falling FF with increasing absorber thickness.⁶⁹

Fig. 6 Contour plots of FF resulting from the sequential change in absorber layer thickness and ETL layer thickness with ETLs including (a) WS₂, (b) C₆₀, (c) PCBM, and (d) TiO₂.

Fig. 7 depicts contour plots that demonstrate changes in PCE for different solar structures when the thickness of the absorber and ETL layers is changed. The ETL WS₂ solar design attained optimal efficiency of 19.71% within the absorber thickness range of 0.50 to 0.65 μm and the ETL thickness range of 0.03 to 0.15 μm shown in Fig. 7a. When the absorber thickness varied from 0.5 to 0.65 μm and the ETL thickness varied from 0.03 to 0.15 μm, the devices that employed TiO₂ ETL also demonstrated an excellent PCE of 19.65%, illustrated in Fig. 7d. According to Fig. 7c, the PCBM ETL also demonstrated consistent PCEs of 19.55%, with an absorber thickness ranging from 0.55 to 0.65 μm and an ETL thickness ranging from 0.03 to 0.085 μm. In contrast to alternative devices, the PSC with C₆₀ ETL demonstrated the lowest PCE of 19.42%, with an absorber thickness between 0.43 to 0.75 μm and an ETL thickness of around 0.03 μm, as seen in Fig. 7b.

Fig. 7 Contour plots of PCE resulting from the sequential change in absorber layer thickness and ETL layer thickness with ETLs including (a) WS₂, (b) C₆₀, (c) PCBM, and (d) TiO₂.

3.4. Variation of absorber layer thickness and defect density on PV performance for Cs₂CuBiBr₆

Since there is a direct relationship between defect density (N_t) and the absorber layer thickness, the entire thickness of the absorber layer has a major impact on the efficient operation of solar cells (SC_S) and photovoltaic (PV) devices.⁶⁸ A decrease in stability and PCE occurs in PSC_S as a result of film disintegration with the creation of pinholes caused by an increase within the defect density (N_t) in the absorber layer.⁷⁰ This section explores the overall effect of defect density (N_t) and absorber thickness on a photovoltaic cell that is based on a Cs₂CuBiBr₆ absorber. Fig. 8–11 shows the results of the simulations that analyzed the effect of different absorber thicknesses (0.4−1.2 μm) and N_t values (1 × 10¹⁵ − 1 × 10¹⁹ cm⁻³) on the PV performance characteristics of the four optimal PSCs.

Fig. 8 Contour plots of V_OC resulting from the concurrent variation in defect density and absorber layer thickness with ETLs including (a) WS₂, (b) C₆₀, (c) PCBM, and (d) TiO₂.

Fig. 8 illustrates the impact contour plot visualization on the V_OC parameter for properties being examined. This visualization was applied to sequentially change the thickness of the absorber layer and N_t. When absorber thickness varies between 0.4–0.8 μm and N_t varies between 1 × 10¹⁵ − 1 × 10¹⁷ cm⁻³, the highest V_OC that can be produced using WS₂-based ETLs is 0.7360 V, as shown in Fig. 8a. The V_OC for TiO₂ ETL-related PSC is 0.7340 V when the absorber thickness is between 0.4–0.8 μm and N_t is between 1 × 10¹⁵ − 1 × 10¹⁷ cm⁻³, depicts in Fig. 8d. A constant V_OC of 0.7320 V was also demonstrated by the C₆₀ ETL, with absorber thicknesses ranging from 0.4–0.8 μm and N_t ranging from 1 × 10¹⁵ − 1 × 10¹⁷ cm⁻³, illustrated in Fig. 8b. Compared to other devices, the PSC with PCBM ETL exhibited the lowest V_OC of 0.730 V, with an absorber thickness varying between 0.4–0.8 μm and N_t between 1 × 10¹⁵ − 1 × 10¹⁷ cm⁻³, as seen in Fig. 8c. It was noted that when absorber thickness was varied with defect densities for WS₂, C₆₀, PCBM, and TiO₂, a similar impact was seen with ETL-based SC configurations.

The effect of changing absorber thickness and defect density on J_SC is demonstrated in Fig. 9a, c and d. When the absorber thickness is between 0.7–1.2 μm and N_t fluctuates between 1 × 10¹⁵ − 1 × 10¹⁷ cm⁻³, the J_SC for WS₂, PCBM, and TiO₂ ETLs achieves 37.30 mA cm⁻². In contrast, at the same thickness of the absorber and N_t ranges, the C₆₀-based optimal device attains a J_SC value of 35.70 mA cm⁻², illustrated in Fig. 9b. Therefore, as the absorber thickness and defect density increase, the J_SC value also increases.

Fig. 9 Contour plots of J_SC resulting from the concurrent variation in defect density and absorber layer thickness with ETLs including (a) WS₂, (b) C₆₀, (c) PCBM, and (d) TiO₂.

Regarding all four structures under consideration, Fig. 10 depicts the impact of varying N_t and absorber layer thickness on FF. When the absorber thickness is between 0.4–0.8 μm and the N_t falls within the range of 1 × 10¹⁵ − 1 × 10¹⁷ cm⁻³, the WS₂-based PSC achieves the highest FF of 79.00%, shown in Fig. 10a. The result for TiO₂ is also similar, according to Fig. 10d. Conversely, the solar cell design based on ETL, C₆₀ shows smaller FF values, measuring 78.80% in cases when the absorber thickness ranges between 0.4–0.8 μm and the N_t value ranges between 1 × 10¹⁵ − 1 × 10¹⁷ cm⁻³, illustrated in Fig. 10b. Similarly, ETL PCBM exhibits the same result in Fig. 10c within the same range of absorber thickness and defect density (N_t).

Fig. 10 Contour plots of FF resulting from the concurrent variation in defect density and absorber layer thickness with ETLs including (a) WS₂, (b) C₆₀, (c) PCBM, and (d) TiO₂.

Finally, the efficiency (PCE) is defined with variations in absorber thickness and defect density (N_t), shown in Fig. 11. According to Fig. 11a and d, the absorber thickness ranges from 0.4–0.8 μm and the N_t ranges from 1 × 10¹⁵ − less than 1 × 10¹⁷ cm⁻³, resulting in the maximum efficiency for WS₂ and TiO₂ being 19.70%. Fig. 11c displays an almost similar PCE of 19.60% for a PCBM-based optimized device when the absorber thickness is between 0.4–0.8 μm and N_t is between 1 × 10¹⁵ − less than 1 × 10¹⁷ cm⁻³. In contrast with the other ETLs in Fig. 11b, the ETL-based solar structure C₆₀ exhibits lower PCE values, recording 18.70% at the same absorber thickness and defect density (N_t) ranges. For every device structure, the optimal thickness of ETLs is a crucial factor in achieving the highest possible PCE value.

Fig. 11 Contour plots of PCE resulting from the concurrent variation in defect density and absorber layer thickness with ETLs including (a) WS₂, (b) C₆₀, (c) PCBM, and (d) TiO₂.

3.5. Impact of absorber layer and HTL layer thickness of several ETLs on PV performance for Cs₂CuBiBr₆

3.5.1. Impact of absorber layer thickness. Perovskite solar cell's efficiency is greatly affected by the thickness of the absorber layer. This impact is significant because it enhances photon absorption, something that's vital for improving the device's general efficiency.⁷¹ Given that the thickness of the absorber affects the performance of the ITO/ETL/Cs₂CuBiBr₆/CBTS/Ni structure, its value was increased from 0.4 to 1.2 μm to optimize the device. Fig. 12a illustrates the relationship between the PSC's performance and the change in the absorber thickness for each of the four distinct ETLs. Almost all designs showed a linear drop with increasing absorber thickness, and the greatest V_OC was approximately 0.73 V, demonstrating that they all performed similarly. The ITO/WS₂/Cs₂CuBiBr₆/CBTS/Ni PSC has the highest V_OC value (0.734 V) compared to other designs, whereas the ITO/PCBM/Cs₂CuBiBr₆/CBTS/Ni PSC has the lowest V_OC value (0.729 V). The WS₂, PCBM, and TiO₂ structures consistently increased with the absorber thickness for J_SC, with values varying from 33.43 to 37.24 mA cm⁻² while the ITO/C₆₀/Cs₂CuBiBr₆/CBTS/Ni PSC exhibited a relatively lower value, ranging from 32.01 to 35.64 mA cm⁻², despite displaying comparable characteristics. For ETL-based structures, the FF decreased linearly when the absorber layer thickness increased; the maximum FF was observed in WS₂, which ranged from 78.95% to 71.66%. TiO₂ and PCBM exhibited a similar trend, dropping from 78.91% to 71.31%, and C₆₀ stayed relatively constant between 78.65% and 71.54%. Regarding PCE, all configurations demonstrated an identical decreasing pattern with increased absorber thickness. When the thickness was 0.6 μm, the WS₂ ETL-based structure had a maximum efficiency of around 19.70%, but the C₆₀-based structure had the lowest efficiency rating, at about 18.69%. When investigating PCBM and TiO₂, it showed that the maximum efficiencies at 0.6 μm were 19.52% and 19.65%, respectively.

Fig. 12 Impact of photovoltaic (PV) variables (PCE, FF, J_SC and V_OC) given the modification in (a) absorber thickness and (b) HTL thickness of Cs₂CuBiBr₆.

3.5.2. Impact of HTL layer thickness. Fig. 12b illustrates the effects of adjusting the thickness of a CBTS HTL with PV characteristics in Cs₂CuBiBr₆-based PSCs, using WS₂, C₆₀, PCBM, and TiO₂ as ETLs. Fig. 12b demonstrates that the V_OC, J_SC, FF, and PCE values for each ETL exhibit comparable patterns with increasing thickness. We only considered CBTS as the HTL in the thickness optimizations, as it was the only material that demonstrated the highest PCE. When the thickness of CBTS increases, the V_OC value for WS₂, C₆₀, PCBM, and TiO₂ as ETLs stays the same at about 0.712 V, 0.709 V, 0.709 V, and 0.711 V. For J_SC, WS₂, PCBM, and TiO₂-based structures showed the highest and identical value of around 35.6 mA cm⁻², with the C₆₀-based structure exhibiting the lowest value of 34.07 mA cm⁻² when the CBTS thickness increased. Considering a value of around 77.57% for the FF and 19.70% for the PCE, the WS₂-based ETL exhibits the maximum value. The PCBM ETL-based solar cell has the lowest FF value, measuring around 77.35%, while the C₆₀-based ETL has the lowest PCE value, measuring about 18.69%, as the CBTS thickness increases. Variation of thickness may have minimal impact if the HTL material has appropriate electrical conductivity and is aligned with the absorber and electrode's energy levels. The precise thickness of the HTL may not have a major impact on performances as long as it efficiently promotes hole transmission. The best possible thickness for greater PCE was found to be 0.1 μm, based on the variation in the HTL thickness. Consequently, 0.1 μm was determined to be the ideal HTL thickness for further analysis, which was also aligned with previous research.⁷²

3.6. Impact of series resistance, shunt resistance and temperature of several ETLs on PV performance for Cs₂CuBiBr₆

3.6.1. Impact of series resistance. Series (R_s) and shunt (R_sh) resistance have a major impact on SCs efficiency and are primarily caused by the relationships across the solar cell layers, the metal contacts on each side, and manufacturing defects.⁵¹ While the effect of R_s ranged from 1 to 6 Ω cm², the shunt resistance was constant at 10⁵ Ω cm² for the four individual perovskite devices, as shown in Fig. 13a. For every single structure of the Cs₂CuBiBr₆ perovskite device, the PCE dropped as the value of R_s changed. The PCE dropped from about 18.62% to 13.41% in devices that used WS₂, PCBM, and TiO₂-based Cs₂CuBiBr₆ perovskites. Concurrently, the PCE of the C₆₀-based Cs₂CuBiBr₆ perovskite device dropped from around 17.71% to 13.08% when the R_s increased. The FF of the ITO/WS₂/Cs₂CuBiBr₆/CBTS/Ni perovskite solar cells (PSCs) dropped from 73.3% to 53.35%. In contrast, the FF values of C₆₀ ETL decreased from 73.31% to 54.2% and PCBM-based structures decreased from 73.09% to 53.18%, correspondingly. On the other hand, the FF value of TiO₂ ETL decreased from 73.25% to 53.29%. Regardless of changes in R_s, the J_SC value remained constant for WS₂, C₆₀, PCBM, and TiO₂ ETL-based structures. The constant values for WS₂, C₆₀, PCBM, and TiO₂ ETL-based structures are around 35.62, 34.06, 35.58, and 35.62 mA cm⁻², respectively. As the thickness of the CBTS increases, the V_OC value stays stable at approximately 0.712 V, 0.709 V, 0.707 V, and 0.711 V when using WS₂, C₆₀, PCBM, and TiO₂ as ETLs. Consequently, in PSCs and modules with large areas, several types of variables, including consistency, R_s and R_sh participate in a decrease with performance, especially within the FF.^73–75

Fig. 13 Impact of photovoltaic (PV) variables (PCE, FF, J_SC and V_OC) given the modification in (a) series resistance (b) shunt resistance and (c) temperature of Cs₂CuBiBr₆.

3.6.2. Impact of shunt resistance. An electrical element called the shunt resistance (R_sh) within the device affects the efficiency of solar cells. Any current that escapes from the active layer, the electrodes, or the region between donors and acceptors is a result of this resistance.⁷² We observed the impact on the PV parameters for the ITO/ETL/Cs₂CuBiBr₆/CBTS/Ni heterostructure with varying R_sh from 10¹ to 10⁶ Ω cm² and a constant R_s of 0.5 Ω cm² in Fig. 13b. A similar trend was observed in the V_OC, FF, and PCE values when R_sh increased. Regardless, for each of the four structures, J_SC is constant. A sudden rise in the V_OC, FF, and PCE values was recorded between 10¹ to 10² Ω cm² of R_sh value. Following this increase, the PV parameters remained constant above a R_sh of 10³ Ω cm². A possible explanation for this might be that, after a certain R_sh threshold is reached, the p–n junction provides a low-resistance route for the flow of junction current.⁵¹ At R_sh value of ≈10² Ω cm², the highest V_OC is 0.7 V, PCE is 19%, and FF is 77%. When R_sh changed, the J_SC values of the WS₂, C₆₀, PCBM, and TiO₂ ETL-based structures remained similar at 35.63, 34.07, 35.59, and 35.62 mA cm⁻², consequently. At 77.55%, the ITO/ETL/Cs₂CuBiBr₆/CBTS/Ni PSC had the greatest FF of all the structures. The PCE value of 19.7% was the highest for the ITO/ETL/Cs₂CuBiBr₆/CBTS/Ni PSC. For optimal device operation, it's necessary to set the series resistance to a minimum and the shunt resistance to a maximum value.⁷⁶

3.6.3. Impact of temperature. Fig. 13c exhibits the effects of operating the device at temperatures ranging from 300 K to 450 K on its performance characteristics. Fig. 13c demonstrates the effects of varying temperatures on four distinct PSC structures. As we varied the temperature, we observed changes in V_OC, J_SC, FF, and PCE across all four structures. Depicted in Fig. 13c, the values of PCE, FF, and V_OC decrease as the temperature increases for almost all structures of optimal solar cells. Conversely, J_SC stays approximately the same across all optimum device structures, regardless of temperature fluctuations. At a temperature of 300 K, the ITO/WS₂/Cs₂CuBiBr₆/CBTS/Ni PSC demonstrated the best efficiency, which was around 19.7%; however, the ITO/C₆₀/Cs₂CuBiBr₆/CBTS/Ni PSC attained the lowest efficiency, which was approximately 18.69%. During this study, the FF of the ITO/WS₂/Cs₂CuBiBr₆/CBTS/Ni PSC dropped from 77.55% to 60.1% as the temperature increased. Moreover, FF dropped for the remaining three PSCs when temperature rose. For all four structures, the J_SC of the PSCs under investigation did not fluctuate with increasing temperature. This indicates that temperature did not have any effect on the J_SC. There was a consistent pattern of decreasing V_OCs with increasing temperature across all four structures. For WS₂, the V_OC values were about 0.712 V, with the lowest at around 0.394 V. When temperatures rose, the reverse saturation current density (J₀) increased, and as a result, the inverse relationship between V_OC and J₀ caused the V_OC values to drop across all ideal device structures. The interaction between V_OC and J₀ is seen in eqn (11).

Previous studies indicate that as the PSC temperature increases, the V_OC value decreases due to the presence of more defects.⁵¹ The bandgap decreased with increasing temperature, which had little effect on the current. However, this alternation appears to remain stable as the temperature rises, despite its small size. The FF and PCE of the device are affected by changes in diffusion length and R_s, which happen as temperature increases.^77,78

3.7. Effect of capacitance, Mott–Schottky, generation and recombination rate of several ETLs on PV performance for Cs₂CuBiBr₆

3.7.1. Effects of capacitance and Mott–Schottky (MS). Fig. 14a shows the capacitance (C) per unit area plot for four solar cells with a bias voltage (V), and Fig. 14b shows the Mott–Schottky (M–S) plot. The charge carrier density (N_d) and built-in voltage (V_bi) can be determined by C–V measurements using the common M–S experimental method. It is used in typical P–N and semiconductor/metal junction devices with space charge regions and fixed depletion layers. The values of the junction capacitance per area (C) are given by eqn (12).

Fig. 14 Distinctions in (a) capacitance (b) Mott–Schottky (c) generation and (d) recombination of Cs₂CuBiBr₆.

According to Fig. 14b, the variables ε_r, q, V, and ε₀ stand for the donor's dielectric constant, electronic charge, applied voltage, and vacuum permittivity, respectively.⁷⁹ V_bi is produced by the prolongation of the linear component to the voltage axis, whereas N_d is produced by the gradient of the linear component. In both scenarios (Fig. 14a and b), the voltage varies between −0.8 to 0.8 V, and the frequency remains constant at 1 MHz. All enhanced devices exhibit an exponential rise in capacitance with increasing applied voltage, as shown in Fig. 14a. At 0.6 V, the solar structures based on WS₂, C₆₀, PCBM, and TiO₂ ETL exhibit an exponential rise. Particularly, the PCBM-based ETL configuration has the greatest capacitance value, at about 710 nF cm⁻². The capacitance value of the C₆₀-based PSC is approximately 661 nF cm⁻², while the WS₂ and TiO₂ ETL-based PSCs have capacitance values of approximately 680 nF cm⁻² and 693 nF cm⁻², respectively. Various ETL-associated solar configurations, as depicted in Fig. 14a, could represent the independent voltage capacitance resulting from the saturation of the depletion layer capacitance. Prior studies have shown that even at low voltages, the current remains substantially below saturation values, and that saturation occurs only at voltage peaks located at the points of contact.⁸⁰ This material has significant prospects as a voltage-controlled solar cell since its capacitance fluctuates as an effect of voltage.

Conversely, the built-in potential (V_bi), which is the difference between the electrode operation and doping level operations, may be effectively and widely determined with the M–S. The p–n junction is the main structure of the M–S theory, with the x-axis intercept usually referring to the V_bi of the semiconductor devices. Different electrode operation functions are used to find the slope of 1/C²(V), which hows the percentage of engaged entrapment centers with lower values as expected.⁸¹

3.7.2. Effects of generation and recombination rate. The generation and recombination rates for four distinct structures are shown in Fig. 14c and d. When the electron moves from the valence band to the conduction band, it creates a hole in the valence band. This process occurs during generation, which involves the production of electron–hole pairs.⁶⁸ Carrier generation is caused by the release of electrons and holes across the process. In all four configurations, Fig. 14c indicates the generation rates peak at around 0.7 μm for the TiO₂ structure. SCAPS-1D utilizes the incoming photon flux N_phot(λ,x) to investigate the formation of electron–hole pairs G(x). It is possible to determine the value of G(x) by using eqn (13), which is derived from the photon flux for point and wavelength.

G(λ,x) = α(λ,x)N_phot(λ,x) (13)

In contrast, the generation rate involves the creation of new electrons and holes in the conduction band, whereas the recombination rate involves their elimination. The lifetime and charge carrier density of a solar cell define its recombination rate. In the initial stages, the existence of defect states inside the absorber layer causes a decrease in the amount of electron–hole recombination. Consequently, the formation of energy levels impacts the electron–hole recombination rate inside the solar cell structure. In this case, WS₂ ETL-based PSCs have a maximum recombination rate of 0.303 μm, shown in Fig. 14d.

3.8. J–V and QE characteristics of Cs₂CuBiBr₆

With voltage ranging from 0 to 0.72 V, Fig. 15a depicts the fluctuating pattern of the J–V characteristics for the four solar cell structures in the investigation. The current density of the C₆₀-associated PSC is roughly 34.07 mA cm⁻², as shown in Fig. 15a, while the J_SC of the PCBM-associated device is almost 35.59 mA cm⁻². The other two ETL-associated devices perform better than the C₆₀ and PCBM-associated devices. In Fig. 15a, the ETL-associated structures of WS₂ and TiO₂ showed an open circuit voltage density of unity and a current density of 35.63 mA cm⁻². The device's efficiency is greatly affected by defects in perovskite films because photoelectrons are created inside these layers. The behavior of electron–hole recombination significantly influences the photovoltaic characteristics of the PSC. The interaction between the J–V curve and the bulk trap density is shown in Fig. 15a for a perovskite film. If defect states exist in perovskite films, there is a significant drop in all photovoltaic films. These findings are consistent with the assumption that perovskite solar structures with a high degree of crystallinity reduce charge recombination and improve performance.⁸²

Fig. 15 Optimization of the (a) J–V characteristic curve and (b) the quantum energy curve of Cs₂CuBiBr₆.

Fig. 15b exhibits the quantum efficiency (QE) graphs for all the devices associated with the research. In this case, the wavelength is changed from 300 to 1100 nm. The exponential increase is seen in Fig. 15b for all structures in the 300 to 360 nm range. The value is consistent across a wide range of around 360 to 600 nm. The QE of the PSCs according to the research at that time was determined to be unaffected by wavelength. Subsequently, the quantum efficiency declines across all structures as the wavelength increases. The QE for the ITO/C₆₀/Cs₂CuBiBr₆/CBTS/Ni PSC in Fig. 15b was slightly lower than that of the other structures. In contrast, regarding wavelength variation, the other three PSCs showed approximately equivalent levels of efficiency. As the thickness of the absorber rises, the quantum efficiency (QE) also rises. This happens because a thicker absorber can absorb more photons.⁸³

3.9. Results from SCAPS-1D are compared to earlier research

The performance characteristics of four device combinations with the recently published optimal configurations are compared in Table 4. Compared to the previously reported Cs₂CuBiBr₆ device structure, Table 4 demonstrates that the optimal Cs₂CuBiBr₆ double perovskite-based solar cell exhibits a higher PCE value. Four sets of device structures were presented with power conversion efficiencies (PCEs) of 19.70%, 18.69%, 19.52%, and 19.65%. In contrast, previously published device structures, such as the FTO/WS₂/Cs₂CuBiBr₆/spiro-OMeTAD/Ag configuration, show a considerably reduced efficiency of around 14.08%.²¹ The exhibited solar structures have greater V_OC levels compared to the published configurations of devices. Conversely, the solar structure that has been given exhibits greater J_SC and FF values than the previously reported Cs₂CuBiBr₆-based device structure. All of the solar structures mentioned have V_OC values over 0.7 V and FF values above 77%, but the device structure that was previously published has the lowest V_OC and FF values. The four solar structures shown in Table 4 performed more effectively than the previously described Cs₂CuBiBr₆-based solar cells.

Table 4 The comparison of PV parameters of Cs₂CuBiBr₆ and similar absorbers-based SCs^a

Type	Optimized devices	VOC (V)	JSC (mA cm^−2)	FF (%)	PCE (%)	Ref.
a E – experimental, T – theoretical.
E	FTO/TiO2/Cs2AgBiBr6/spiro-OMeTAD/MoO3/Ag	1.01	3.82	65	2.51	84
E	FTO/c-TiO2/mTiO2/Cs2AgBiBr6/N719/spiro-OmeTAD/Ag	1.06	5.13	—	2.84	85
E	FTO/TiO2/Cs2AgBiBr6/spiro-OMeTAD/Au	1.511	3.89	51.76	3.04	86
T	ITO/SnO2/Cs2AgBiBr6/spiro-OMeTAD/Au	0.92	11.4	60.93	6.37	87
T	FTO/WS2/Cs2CuBiBr6/spiro-OMeTAD/Ag	0.60	34.59	67.36	14.08	21
T	FTO/TiO2/Cs2AgSbBr6/spiro-OMeTAD/Ag	0.94	22.49	50.2	10.69	21
T	ITO/WS2/Cs2CuBiBr6/CBTS/Ni	0.712	35.63	77.57	19.70	This work
T	ITO/C60/Cs2CuBiBr6/CBTS/Ni	0.709	34.07	77.39	18.69	This work
T	ITO/PCBM/Cs2CuBiBr6/CBTS/Ni	0.709	35.59	77.35	19.52	This work
T	ITO/TiO2/Cs2CuBiBr6/CBTS/Ni	0.711	35.62	77.52	19.65	This work

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The performance parameters of the four device configurations that were presented in Table 4 are compared to the optimum configurations that were recently published. In comparison to the previously reported Cs₂B′B′′Br₆ device structure, Table 4 demonstrates that the optimal Cs₂CuBiBr₆ double perovskite-based solar cell exhibits a greater PCE value. In Table 4, the fifth solar cell device structure used spiro-OMeTAD HTL, resulting in 14.08% efficiency compared to our present study of HTL CBTS. The emphasis of our investigation was on the properties of the absorber, such as its defect density, which were different from those of previous theoretical research on device structures. The characteristics of our study's ETL and HTL combinations also differed from those used in previous theoretical assessments. The optical characteristics of the absorber also influence the absorption of solar energy. By achieving 14.08% PCE in the FTO/WS₂/Cs₂CuBiBr₆/spiro-OMeTAD/Ag structure, the improved optical characteristics of the Cs₂CuBiBr₆ absorber were observed.²¹ The above justifies the conclusion that, compared with previously researched Cs₂CuBiBr₆-based, differently structured solar cells, our Cs₂CuBiBr₆ solar cell exhibits superior PCE.

4. Conclusion

The research objective is to investigate the SCAPS-1D simulation results and determine the possibility of developing perovskites based on cesium copper bismuth bromide. The four solar designs (ITO/WS₂/Cs₂CuBiBr₆/CBTS/Ni, ITO/C₆₀/Cs₂CuBiBr₆/CBTS/Ni, ITO/PCBM/Cs₂CuBiBr₆/CBTS/Ni, ITO/TiO₂/Cs₂CuBiBr₆/CBTS/Ni) are compared in terms of their PV properties. Among all the investigated structures, ITO/WS₂/Cs₂CuBiBr₆/CBTS/Ni demonstrated the greatest performance with PCE of 19.70%, V_OC of 0.712 V, J_SC of 35.63 mA cm⁻², and FF of 77.57%. An advantageous band alignment is responsible for this higher performance. The absorber layer falls within the range of 0.4 to 1.2 μm, with the highest efficiency occurring at 0.6 μm. The thickness of the electron transport layers (ETLs) varies between 0.03 and 0.15 μm for the four different perovskite solar cell structures. Device efficiency is further improved by optimizing the HTL thickness between 0.1 and 0.5 μm. PV characteristics are greatly impacted by changes in defect density (N_t), whereas PCE and FF are adversely affected by series resistance without significantly impacting J_SC and V_OC. While V_OC, FF, and PCE increase with shunt resistance, enhancing at 10² Ω cm², the J_SC stays constant. From 300 to 450 K, the performance of WS₂-based ETL structures remains preferable; as the temperature rises, PCE, V_OC, and FF drop but J_SC stays constant. In particular, at around 710 nF cm⁻², the PCBM-based ETL structure has the highest capacitance value. When the rates of generation and recombination were investigated, the ITO/WS₂/Cs₂CuBiBr₆/CBTS/Ni structures exhibited the maximum recombination at 0.303 μm and the ITO/TiO₂/Cs₂CuBiBr₆/CBTS/Ni configurations showed the most generation at 0.7 μm. J–V characteristics and quantum efficiency (QE) analysis both demonstrated superior performance WS₂ ETL devices. For the development of double perovskite-based innovations, these outcomes provide significant information for improving solar cell designs.

Data availability

Data will be made available on request.

Author contributions

Khandoker Isfaque Ferdous Utsho: investigation, methodology, data curation, conceptualization, writing original manuscript; S. M. G. Mostafa: investigation, methodology, data curation, review-editing; Md. Tarekuzzaman: formal analysis, software, conceptualization, review-editing; Muneera S. M. Al-Saleem: formal analysis, methodology, data curation, review-editing; Nazmul Islam Nahid: formal analysis, methodology, data curation, review-editing; Jehan Y. Al-Humaidi: formal analysis, methodology, data curation, review-editing; Md. Rasheduzzaman: formal analysis, validation, review-editing; Mohammed M. Rahman: formal analysis, validation, supervision, review-editing; Md. Zahid Hasan: formal analysis, validation, supervision, review-editing.

Conflicts of interest

There is no conflict to declare.

Acknowledgements

This research is funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R80), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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