A numerical investigation to design and performance optimization of lead-free Cs₂TiCl₆ based perovskite solar cells with different charge transport layers

Abstract

Among the most attractive light-absorbing materials, halide perovskites have been gaining popularity for their versatile range of use in solar cells, lasers, and photodetectors. Whereas, Titanium (Ti)-based all-inorganic perovskite solar cells (PSCs) have garnered attention for their optoelectronic capabilities in response to this situation. In this theoretical study, Cesium Titanium (IV) Halide based lead-free, eco-friendly, and stable Cs₂TiCl₆-based PSC has been proposed and a numerical simulation using SCAPS-1D has been carried out to enhance the cell performance by optimizing the device parameters. A different set of hole transport layers (HTLs) like MoO_3, ZnTe, CNTS, CuAlO_2, CdTe, nPB, C₆TBTAPH_2, N: TiO_2, NiCo₂O_4, and PBTTT-C14 was simulated in combination with electron transport layers(ETLs) such as CdS, Nb₂O₅, ZnSe, and MZO. After several cell optimizations like thickness, acceptor, donor, and defect concentration of selected four structures, the best cell structure are suggested e.g., FTO/CdS/Cs₂TiCl₆/CdTe/Au that shows a PCE of 18.15% along with the short circuit current density (J_SC) of 17.83 mA/cm², open-circuit voltage (V_OC) of 1.188 V, fill factor (FF) of 89.51%. Among all devices, the solar cell performance decreases when series resistance (R_S) and temperature are increased as opposed to shunt resistance (R_Sh). The obtained results reveal that Cs₂TiCl₆-based PSC can contribute to the advancement of efficient non-toxic, all-organic perovskite solar cells in the future.

 Introduction

A significant proportion of residential areas in the contemporary global context get uninterrupted exposure to sunlight throughout the year. Energy generated from the sun is abundant, and it provides efficient energy that makes solar power energy a good alternative to limited fossil fuels to mitigate the future energy demand¹. Scientists are conducting various kinds of research to discover the most effective, environment-friendly, low-cost, etc. devices for renewable energy resources². Among them, photovoltaic (PV) cells are considered top-notch among these sustainable energy sources, possessing the complete capability to fulfill the aforementioned criteria^3–5.

As regards the production of solar energy, silicon-based solar cells (SCs) have cemented their top position with a share of 95% in the present PV market with laboratory power-conversion efficiency (PCE) over 25%⁶. Despite these extensive advancements in SC technology, the production costs related to Si-based solar cells could not be minimized due to the usage of cleanroom technology, thus increasing the costs of those applications^6,7. When researchers worldwide are in search of an alternative to silicon solar cells, halide-based perovskite solar cells (PSCs) have appeared as a replacement, showing exceptional photoelectric implementation, higher electrical constraints for instance quantum efficiency (QE), current density, and lower manufacturing rate^8–11. Recent studies have shown an increment of using lead (Pb) halide PSCs, recorded PCE of 25.6%¹², because of their ideal bandgap, affordability, higher absorption coefficient, and long carrier diffusion length. However, there are two main concerns for the commercial applications of Pb-based PSCs e.g. (i) the toxicity of lead affects the ecosystem, and (ii) the instability of devices caused by organic citations^13,14. In these circumstances, Tin (Sn⁺²) ^15,16, Germanium (Ge⁺²)¹⁷, Bismuth (Bi⁺³) ^18,19, and Palladium (Pd⁺⁴)²⁰ are considered replacement of toxic lead in practical SC usage. However, it was reported by Babayigit et al. that Sn-based halide perovskites also are responsible for large amounts of poisonous elements²¹. Moreover, upon contact with air, Sn⁺² also transforms to Sn⁺⁴ for oxidation. Thus, a special kind of PSCs has been a subject of interest for researchers in finding stable and non-toxic perovskites²².

A novel group of halide perovskites, centered around Titanium (Ti) (IV), and particularly exemplified by Cs₂TiCl₆, has been documented as a potential material for the field of SC applications where Ti is a substitution of hazardous Pb. Because of the enduring oxidation state stability of titanium, Cs₂TiCl₆ can absorb thermal stress and can be utilized in challenging hazy environments making it the best candidate for Pb-free PSCs. Chakraborty et al. examined the Cs₂TiCl₆ absorbing layer and revealed its thickness and indirect band gap are 1.0 μm and 2.9 eV, respectively²³. The report analyzed the electronic and optical properties of Ti-based PSC and illustrated that Cs₂TiCl₆ is compatible with PV and optoelectronic implementations²⁴. While Moiz et al. optimized his proposed device and showed a maximum PCE of roughly over 18.5%⁴. A contrastive analysis was conducted by Mokhtari et al. and found that Cs₂TiCl₆ indicates a high absorption coefficient of 10⁵ cm⁻¹ in the visible light region ²⁵. There have been few investigations conducted on Cs₂TiCl₆, and determining its optimal device architectures has been an appealing subject for experts in recent years. In order to achieve an effective PV response, the perovskite absorber layer positioned itself between the charge transport layers like the electron transport layer (ETL) and hole transport layer (HTL). Most importantly, the highest PV can be attained when the charge carriers are distributed uniformly within SCs^7,26. The outcome of PSCs is extensively determined by the ETL and HTL since these layers play a significant role in various processes such as charge carrier extraction, transport, and recombination. Thus, It is of paramount importance to select the ETL with suitable band alignment, excellent electron mobility, sufficient light transmittance, and resistance to moisture^27–29. In this work, four ETLs such as cadmium sulfide (CdS), Niobium pentoxide (Nb₂O₅), Zinc selenide (ZnSe), Magnesium zinc oxide (MZO) in conjunction with preferred and compatible HTLs like as Nitrogen-Doped Titanium Dioxide (N: TiO₂)³⁰, n-Propyl Bromide (nPB)³¹, Nickel cobaltite (NiCo₂O₄), Molybdenum trioxide (MoO₃)³², Poly(2,5-bis(3-tetradecylthiophen-2yl)thieno(3,2-b)thiophene) (PBTTT-C14)³³, Copper Aluminum Oxide (CuAlO₂)³⁴, Zinc telluride (ZnTe)³⁵, Carbon nanotubes (CNTS)³⁶, Copper zinc tin sulfide (CZTS), Cadmium telluride (CdTe)³⁷, Octahexyltetrabenzo Triazaporphyrin (C₆TBTAPH₂)³⁸ are optimized to figure out the best combinations of PSC. The selection of ETL and HTL materials in this study was guided by several key factors, including band alignment with Cs₂TiCl₆, chemical stability, and interface compatibility. CdS³⁹, Nb₂O₅⁴⁰_, ZnSe⁴¹, and MZO⁴² were chosen as potential ETLs due to their conduction band levels being well-aligned with the conduction band minimum of Cs₂TiCl₆, promoting efficient electron extraction. In addition, these materials are known for their thermal and environmental stability, and have been successfully employed in similar n–i–p architectures. CdTe⁴³ was selected as the HTL because of its deep valence band, which supports effective hole transfer from Cs₂TiCl₆, while blocking electrons, thereby enhancing charge selectivity and minimizing recombination losses.

The experimental feasibility of Cs₂TiX₆-based perovskites has been increasingly validated by recent studies. Chakraborty et al. successfully synthesized Cs₂TiX₆ (X = Cl, Br, I, F) compounds and demonstrated through comparative experimental and DFT investigations that Cs₂TiBr₆ and Cs₂TiCl₆ exhibit favorable bandgaps, material stability, and visible light absorption, with TEM and SAED analyses confirming high crystallinity⁴⁴. Furthermore, Chen et al. reported the fabrication of high-quality Cs₂TiBr₆ thin films via a low-temperature vapor-based method, achieving excellent intrinsic and environmental stability, long carrier diffusion lengths, and stable photovoltaic performance with efficiencies up to 3.3%⁴⁵. Additionally, Ju et al. demonstrated that Ti-based vacancy-ordered double perovskite halides such as Cs₂TiI_xBr_6−x possess tunable bandgaps (1.38–1.78 eV), high stability, benign defect properties, and strong optical absorption, making them highly promising for single-junction and tandem solar cell applications⁴⁶. These experimental advances highlight the viability of synthesizing Cs₂TiCl₆-based devices and provide a strong foundation for their further development in eco-friendly, stable, lead-free photovoltaic technologies.

With the desire to build environment-friendly, non-poisonous, comparatively stable, highly efficient SCs, the one-dimensional solar cell capacitance simulator software, SCAPS 1D^47–50, is employed to lead a thorough assessment of different parameters of PV performance for Cs₂TiCl₆-based PSC. This work initially examined 10 compatible HTLs that were optimized to determine the most favorable results, while keeping the CdS ETL constant. The resulting structure was then compared with additional ETLs, namely Nb₂O₅, ZnSe, and MZO. Subsequently, the thickness of the absorber and HTL, acceptor density and defect density of the absorber, donor density of ETL, and acceptor density of the HTL are tuned in a sequential manner. Simultaneously, the impact of absorber and HTL thickness, as well as absorber defect and acceptor density, on the PV characteristics is examined. Moreover, the enhanced performance of the four devices is supported by evaluating their current-voltage density, quantum efficiency, resistance, operating temperature, and generation and recombination rate. The device structure that produced the most outstanding PV parameters is refined further to surpass the efficiency of the PSC configuration.

 Numerical simulations

It was discussed above that the SCAPS-1D is a one-dimension (1-D) PV simulator advanced with C programming language was designed by Marc Bargeman and his co-workers at the University of Gent, Ghent, Belgium)^51–53. A seven-layer SC stack has been developed into this programming software thus including some significant PV parameters (like thickness, defects, doping density, etc.)^51,54. The SCAPS-1D has been employed for simulating the PSCs in previous literature^55–59. The mechanism of this software is fundamentally established on four sets of PV equations, i.e., Poisson equation, continuity equations, charge transport equations, and absorption coefficient equation (for both electrons and holes) are described as follows:

The Poisson equation (Eq. 1) implies the behavior of electrical potential (φ) that includes how different types of electrical charges are circulated inside of SC. The electric charge constant is defined as q, it is valued at 1.602 × 10⁻¹⁹ C. While the absolute dielectric constant, relative dielectric constant of each layer’s material, donor/acceptor doping density, hole/electron density distribution, and the hole/electron density distribution (in terms of thickness x) are classified with $\:{\epsilon\:}_{0}$, $\:{\epsilon\:}_{r}$, $\:{N}_{\text{A}}/{N}_{D}$, $\:{\rho\:}_{p}/{\rho\:}_{n}$ and p(x)/n(x), respectively.

$$\:v\frac{{d}^{2}\:{\upvarphi\:}\left(\text{x}\right)}{d{x}^{2}}=\left(\frac{q}{{\epsilon\:}_{0}{\epsilon\:}_{r}}\right)(\:p\left(x\right)-n\left(x\right)+{N}_{D}-{N}_{A}+\:{\rho\:}_{p}-{\rho\:}_{n})$$

(1)

.

The derivative of hole current density ($\:{J}_{\text{P}}$) and electron current density ($\:{J}_{\text{n}}$) with respect to position variable x is denoted in terms of carrier generation (G), and carrier recombination (R) known as the continuity equation (Eqs. 2 and 3).

$$\:\frac{d{\text{J}}_{\text{n}}}{dx}=G-R$$

(2)

$$\:\frac{d{\text{J}}_{\text{P}}}{dx}=G-R$$

(3)

.

The charge transport equations can be written as follows Eqs. 4 and 5 where µ_p (hole) and µ_n (electron) are free charge carrier mobility. Meanwhile, electron and hole charge diffusion co-efficient are distinguished with $\:{D}_{\text{n}}$ and $\:{D}_{\text{P}}$ in the order given in Eqs. 4 and 5.

$$\:{\text{J}}_{\text{n}}={D}_{\text{n}}\frac{\text{d}\text{n}}{\text{d}\text{x}}+{{\upmu\:}}_{\text{n}}\:\frac{\text{d}\varnothing\:}{\text{d}\text{x}}$$

(4)

$$\:{\text{J}}_{\text{P}}={D}_{\text{P}}\frac{\text{d}\text{p}}{\text{d}\text{x}}+{{\upmu\:}}_{\text{P}}\:\frac{\text{d}\varnothing\:}{\text{d}\text{x}}$$

(5)

.

With regards to projecting the absorption coefficient, several designs are available in the algorithm of SCAPS-1D software because of the presence of varieties of semiconducting materials. The optical absorption coefficient model for PSCs can be graded in mathematical ways like Eq. 6, where A, and B are constant, h = 6.62607015 × 10⁻³⁴ JHz⁻¹, ν is the frequency of photons and $\:{E}_{\text{g}}$ is the absorber layer’s band gap.:

$$\alpha (\lambda )~ = ~(A~ + ~~\frac{B}{{h\vartheta }}\sqrt {h\vartheta - Eg} ~)$$

(6)

.

Therefore, utilizing the optimum conditions and the above equations SCAPS-1D is used in this simulation to determine the parameters of suggested PSCs such as open-circuit voltage (V_OC), short-circuit current density (J_SC), fill factor (FF), PCE, and QE.

 Cs₂TiCl₆-based PSC structure

The architecture of the layered Cs₂TiCl₆-based solar cells investigated in this study follows an n–i–p planar heterojunction configuration, as illustrated in Fig. 1. In this design, ETL is positioned in the n-region, the perovskite absorber layer (Cs₂TiCl₆) occupies the intrinsic (i) region, and HTL is located in the p-region. Upon solar illumination, the perovskite layer generates excitons—bound electron-hole pairs. The dissociation of these excitons occurs primarily at the interfaces between the i-region and the adjacent n- and p-regions, where built-in electric fields assist in separating the charge carriers. Specifically, electrons are driven toward the ETL (n-region), while holes migrate toward the HTL (p-region). The effective separation and transport of these carriers are governed by their respective diffusion lengths and the internal electric field, ensuring efficient charge collection at the corresponding electrodes. The charge transfer characteristics at the HTL/perovskite interface critically influence the efficiency and stability of perovskite solar cells (PSCs). Interfaces can be smooth or rough, with roughness potentially causing charge trapping, increased recombination, and reduced carrier mobility. While smooth interfaces generally promote efficient carrier transport, moderate roughness does not always degrade performance. For instance, Richter et al. showed that moderate interface roughness in CIGSSe solar cells improved optical absorption and carrier collection, leading to enhanced Jsc, Voc, and FF despite slightly higher recombination. Rough interfaces also increase junction capacitance, which must be considered in device analysis⁸. Other studies have intentionally introduced controlled roughness to enhance light scattering and absorption, though excessive roughness can negatively impact charge transport⁶⁰.

Titanium-based Pb-free halide PSCs, Cs₂TiCl₆, gold (Au), and Fluorine-doped Tin Oxide (FTO) are employed as an absorber, back contact metal, and transparent conductive oxide (TCO), individually during that experimentation. Furthermore, to determine the best structure for the PSC, four ETLs (such as CdS, Nb₂O₅, ZnSe, and MZO) and 10 HTLs (like MoO_3, ZnTe, CNTS, CuAlO_2, CdTe, nPB, C₆TBTAPH_2, N-TiO_2, NiCo₂O_4, PBTTT-C14) are investigated from 36 various combinations to determine the best structure for the PSC. A stable version 3.3.10 of SCAPS-1D is implemented for device modeling and optimization of PSC under room temperature of 300 K and AM.1.5 solar spectrum (light intensity 1000 W/m²) in this study. The input parameters used in this simulation are given in Tables 1, 2 and 3. The material parameters used in this simulation, including bandgap energy, electron affinity, dielectric constant, carrier mobilities, and defect densities, were primarily adopted from experimentally reported studies and validated computational research^61,62. This approach ensures that the numerical results accurately represent realistic device behavior and maintain consistency with observed material properties.

Fig. 1

Device Configuration of Cs₂TiCl₆-based multilayered PSCs.

Table 1 Properties of FTO, perovskite (Cs₂TiCl₆) and etls.

Table 2 Features of htls.

Table 3 Input parameters of interface defect layers⁷⁷.

 Result and discussion

Effect of HTL variation

The hole transport material acts as a compelling element for the successful reversal of oxidation states between the conducting hole and light absorber in PSCs. In addition, the physical location change of holes from the absorber layer to rear contact is assisted by the HTL in Perovskite cell configurations^78,79. To interpret the influence of HTL on the PV parameters of the device, 10 HTLs such as MoO₃, ZnTe, CNTS, CuAlO₂, CdTe, nPB, C₆TBTAPH₂, N: TiO₂, NiCo₂O₄, and PBTTT-C14 are utilized considering CdS as ETL. The PV features for instance PCE, V_OC, FF, and J_SC are illustrated in Fig. 2 in this study.

Fig. 2

Impact of different HTLs on PSC parameters when CdS is used as ETL.

The highest percentage of FF (77%) is observed by CNTS as opposed to the lowest, 60% is accounted for by N: TiO₂. The remaining HTLs show the range of 67–85% FF throughout the simulation. In terms of V_OC, around 0.87 V is obtained by CdTe which is the minimal in this particular device. The surprising fact is that MoO_3, N: TiO_2; and PBTTT-C14 display the same voltage of about 1.35 V while CuAlO₂ has shown a superior voltage at 1.79 V. On the other hand, the maximal short circuit current has been recorded for CdTe, at 20 mA/cm², whereas 4 HTLs, for instance, MoO₃, ZnTe, CuAlO₂, nPB, NiCo₂O₄, and PBTTT-C14 are exhibited the least of J_SC e.g., 0.9 mA/cm². The remaining two HTLs, C₆TBTAPH₂ and CNTS have reported 1.0 mA/cm² and 1.2 mA/cm², respectively. As regards PCE, CdTe has notched up 14.5% of PCE and contrarily the minimum PCE (7.3%) has accounted for the N: TiO₂. The rest ratio of PCE is altered between 8% and 13.8% to the residual HTLs.

 Device optimization

Optimization of absorber layer thickness

The absorber layer thickness plays a noteworthy role in inducing the lifetimes and diffusion lengths of generated charge carriers^80,81. To stimulate the effect on PV constraints, the absorber layer thickness differed from 0.4 μm to 1.15 μm, while the thickness of ETL and HTL remained unaffected as represented in Fig. 3a

Fig. 3

Influence of thickness of absorber a and HTL b on PSC device performance.

For Nb₂O₅-based PSC, when the thickness was enhanced, the V_OC declined from 0.98 V to 0.91 V and the FF and J_SC experienced a slight rise by 1.5% (in magnitude) and by 0.2 mA/cm². In addition, the SC efficiency did not show any changes but remained unchanged as absorber thickness increased.

For CdS-based devices, on the other hand, the V_OC, and J_SC increased very negligibly while the FF and PCE decreased barely with the enhancement of the absorber layer. Similarly, ZnSe and MZO-based SC configurations also showed homogeneous graphs for PV parameters when the absorber layer was mostly thickened. So, the ideal absorber layer thickness was obtained to be 500 nm in this study in order to gain the superior performance of each device. This value was implemented for the later parts of this research.

 Optimization of HTL layer thickness

The significance of HTL layer thickness upon different PV parameters is represented in Fig. 3b when the thickness ranges from 10 nm to 500 nm. To figure out the optimum thickness of HTL, the ETL thickness and optimized absorber thickness were fixed. As the HTL was increased, the V_OC for Nb₂O₅-based device surged to 0.94 V compared to 0.86 V for CdS, ZnSe, and MZO-based structures, the J_SC of all devices escalated considerably from 12 mA/cm² to 26 mA/cm². With regards to FF, there was a slight plunge (by 7%) to the Nb₂O₅ device from 10 nm to 200 nm HTL thickness, then it remained stable. However, the remaining three devices corresponded that there was no reliance on the thickness of HTL because the graph was literally flat. However, when the thickness of HTL enlarged, the PCE of CdS, ZnSe, and MZO-based devices jumped to 18% (in magnitude) in comparison with the Nb₂O₅ device (14%). A thinner HTL may not provide complete coverage of the absorber layer, leading to increased recombination at the interface. As the thickness increases, hole extraction becomes more efficient, improving Voc and FF. However, excessive thickness results in higher resistive losses, thereby reducing the overall efficiency. In this circumstance, 200 nm was chosen to be the optimum HTL thickness which was followed for the next phases of this study. Increasing the thickness initially enhances the electron extraction and transport, thereby reducing recombination at the interface. However, beyond an optimal thickness, the series resistance increases, which limits current flow and reduces both the short-circuit current (Jsc) and fill factor (FF). Due to the purpose of avoiding recombination of charge carriers, the thickness of ETL should be less than the thickness of HTL⁸².

Influence of absorber and HTL thickness on cell performance

The contour diagram Fig. 4 depicts the evaluation of the cell efficiency by simultaneously modulating the absorber thickness and CdTe HTL thickness of Cs₂TiCl₆-based PSC with four different ETLs. According to Fig. 4a, 16.46% PCE was obtained for CdS ETL used PSC when the thickness of absorber and CdTe HTL were from 0.5 to 1.0 μm and 0.23 to 0.30 μm, respectively. However, Nb₂O₅ was taken as ETL; the device showed in Fig. 4b the lowest 13.75% PCE, since changing the absorber thickness up to 1.0 μm, the thickness of CdTe HTL was ≥ 0.22 μm. It was observed in Fig. 4c that the ZnSe-associated SC and the device configuration with MZO as ETL in Fig. 4d documented the exact same percentage of PCE (16.46%) as the CdS-based device showed when increasing the thickness of absorber ≥ 0.5 μm and thickness of CdTe HTL was greater than 0.23 μm.

Fig. 4

Contour mapping of PCE with respect to the thickness of the Cs₂TiCl₆ and CdTe HTL.

 Influence of absorber defect density and acceptor density on PCE

The change of perovskite cell efficiency by varying the acceptor density (N_A) and defect density (N_t) of the absorber has been demonstrated for four studied structures in Fig. 5. When CdS was used as ETL shown in Fig. 5a, the structure had 16.62% PCE with N_A fluctuating between 10¹⁴ cm⁻³ and 10¹⁹ cm⁻³ and N_t was increased till 10¹⁵ cm⁻³. As indicated by Fig. 5b, among all configured devices, Nb₂O₅ ETL accounted for the lowest PCE of 14.78% when acceptor concentration was 10¹⁴ ≤ N_A ≥ 10¹⁹ cm⁻³ but defect density (N_t) went up to less than 10¹⁵ cm⁻³.

Fig. 5

Contour mapping of PCE with respect to varying absorber defect density (N_t) and acceptor density (N_A) for a CdS, b Nb₂O₅, c ZnSe, and d MZO ETL configured devices.

In addition, 16.66% SC efficiency was recorded in Fig. 5c for devices with ZnSe ETL while N_t was increased just above 10¹⁵ cm⁻³ but N_A oscillated from 10¹⁴ to 10¹⁹ cm⁻³. However, in comparison with other configurations, the PSC with MZO ETL Fig. 5d witnessed the highest efficiency of 16.67% as long as the N_t and N_A of the absorber intensified up to 10¹⁵ cm⁻³, between 10¹⁴ and 10¹⁹ cm⁻³, respectively. Since the PV performance of PSC together depends on PCE, FF, V_OC, and J_SC, the increasing value of N_t and N_A raised the efficiency performance to a certain limit upon the selection of absorber and HTL material which is relevant to the previous study ⁸³.

Band alignment

Fig. 6

Energy band diagram of Cs-based PSCs with CdTe as the HTL and a CdS, b Nb₂O₅, c ZnSe, and d MZO as ETL.

The alignment of energy levels exhibits a substantial impact on the performance and effectiveness of PSC. It has been developed using each ETL paring with Cs₂TiCl₆ absorbing layer and CdTe as HTL that enhances influence on the difference in valence band (VB) levels between the HTL and the absorber layer and the conduction band (CB) levels between the ETL and the absorber layer. Within the framework of PSCs, photo-excited electrons are concurrently driven into the CB of the ETL, while positively charged holes make their way to the HTL. Afterward, electrons and holes converge at the front layer (FTO) and back (Au) contact metals, individually. To ensure the safe extraction of electrons at the interface between ETL and Cs₂TiCl₆, the ETL requires an increased electron affinity compared to Cs₂TiCl₆. Simultaneously, the ionization energy of the HTL must be lower than that of Cs₂TiCl₆ for efficient hole extraction at the point of contact between Cs₂TiCl₆ and the HTL. Furthermore, the unstable energy band at both intersections has a significant influence on the PV parameters of the device. In Fig. 6, quasi-fermi levels (F_n and F_p) are combined with CB energy (E_C) and VB energy (E_V), respectively. The F_P was placed at a high up of E_V in every ETL while F_n and E_C are comparatively proportionate to each other. The band gap of Cs₂TiCl₆ was 2.33 eV while the band gaps of CdS, Nb₂O₅, ZnSe, and MZO were 2.4 eV, 3.46 eV, 2.81 eV, and 3.3 eV, respectively. Conversely, comparatively minimal performance has been found for CdS and ZnSe ETLs because of their corresponding band gaps. CdS, ZnSe, and MZO exhibit better conduction band alignment with the Cs₂TiCl₆ absorber layer, which facilitates efficient electron extraction and suppresses interfacial recombination. In contrast, Nb₂O₅ has a deeper conduction band minimum that creates a larger offset with the absorber’s conduction band, resulting in a less favorable energy alignment for electron transport.

 Optimization of acceptor density of the absorber

Fig. 7

Trends in device performance (PCE, FF, V_OC, and J_SC) with absorber acceptor density and defect density.

For the purpose of gathering meaningful insights into the impact of absorber acceptor density (N_A) on PV parameters, the N_A of Cs₂TiCl₆ for four optimized devices was altered, ranging from 10¹⁴ cm⁻³ to 10¹⁹ cm⁻³ as represented in Fig. 7a. It has summarized how the PCE, FF, V_OC, and J_SC were modulated with the variance of N_A while other variables of the absorber layer were considered constant.

To begin with, there was not any distinguishable change in all PV features when the N_A was less than 10¹⁸ cm^{−3 84}. That implies the unchanging direction for the generation rate of photo-generated carriers with N_A when same the number of photons is accrued ^55,85. For increasing the acceptor concentration of the Cs₂TiCl₆ layer, afterward, the J_SC remained unchanged for all of the Cs₂TiCl₆-based SCs except Nb₂O₅-based PSC which had an abrupt increase to 22.5%. As regards V_OC, a similar trend to J_SC, from 0.86 V to 0.94 V, was observed for Nb₂O₅ designed PSC; the other PSCs maintained their respective initial values as N_A increased. The reason behind the V_OC rise is due to the fall of the fermi energy level of the hole and the increase of built-integrated potential⁸⁴. When the N_A value of the absorber further extended above 10¹⁸ cm⁻³, Nb₂O₅-based SCs accumulated a sudden decline from 15 to 13.5% (in magnitude) for cell efficiency (η) and 23% (in magnitude) downturned for FF. As a result, to acquire better outcomes for each combination, the optimum value of N_A of Cs₂TiCl₆ was selected as 10¹⁶ cm⁻³ which was utilized next periods of this simulation.

Optimization of defect density of the absorber

The illustration in Fig. 7b shows how the variation of defect density of the absorber (N_t) has influenced the device performance. The N_t of the Cs₂TiCl₆ absorber layer was inspected for selected structures on the scale of 10¹⁴ cm⁻³ to 10¹⁹ cm⁻³. With the increasing N_t value, there was a deterioration in SC features like η, FF, V_OC, and J_SC. As reported by this observation, the values of V_OC, J_SC, and PCE got stable till the N_t attained at 10¹⁵ cm⁻³ but the FF remained uniform at 10¹⁹ cm⁻³ of defect density for all optimized configurations. Then N_t of 10¹⁵ cm⁻³ onwards, V_OC, J_SC, and PCE displayed a similar kind of decrement such as from 0.855 V to 0.848 V, from 21 mA/cm² to 16 mA/cm², also from 15.5 to 12%, respectively when Nb₂O₅ was installed as ETL. Conversely, CdS, ZnSe, and MZO-based SCs exhibited maximum PCEs of 17.6% on average (in magnitude) at their individual best N_t. Ultimately at 10¹⁹ cm⁻³ of N_t, the distinct cell efficiency was reduced to 12.7% on average. The declined efficiency of the structures was subjected to the non-radiative Shockley-Read-Hall (SRH) recombination, thus causing diminishing carrier lifetimes, increased recombination rates, and a substantial reduction in the overall performance of the device ⁸⁶. Decreasing N_t provides the best PCE, but it can be ignored as optimum value because it is a daunting task to integrate a material experimentally⁸⁴. These findings were nearly commensurable to the previously published research work⁸⁷. Therefore, the optimum N_t of the Cs₂TiCl₆ absorber was taken as 10¹³ cm⁻³. This value was maintained in the following steps of this study. A significant body of experimental data suggests that polycrystalline thin films of lead halide perovskites usually demonstrate defect densities around 10¹⁵–10¹⁶ cm⁻³ while single crystals generally show bulk defect densities of 10¹² cm⁻³ or lower ^88,89. In this study, the defect density of the perovskite absorber has been varied from 10¹⁴ cm⁻³ to 10¹⁹ cm⁻³ and the optimized defect density of the device was found to be 10¹³ cm⁻³, which aligns well with experimentally reported values for perovskite solar cells. For example, Heo et al. demonstrated a device efficiency of 13.5% with CH₃NH₃PbI₃ having a defect density of 1.3 × 1015 cm^{−3 90}. Another study reported trap densities of 5.65 × 10¹⁵ and 2.25 × 10¹⁵ cm⁻³ where the lowest trap density (2.25 × 10¹⁵ cm⁻³) corresponded to the highest PCE ⁹¹. These comparisons confirm that our defect density is within a realistic and competitive range for efficient solar cell operation.

Optimization of donor density of ETL

Fig. 8

Analysis of a donor density (N_D) of ETL, and b acceptor density (N_A) of HTL.

The representation of Fig. 8a states the modulation of PCE, FF, V_OC, and J_SC with respect to changing the donor density (N_D) of ETL. To gain better effectiveness, the N_D of ETL was adjusted within the range of 10¹⁵ cm⁻³ to 10²⁰ cm⁻³. In this investigation for all device structures, it is evident that FF was stable all through the variation of donor density of ETL. Whereas, the V_OC encountered different patterns among all executed ETLs where CdS, ZnSe, and MZO-installed devices got unaltered apart from Nb₂O₅–based PSC that had a slight increase between N_D of 10¹⁸ cm⁻³ to 10²⁰ cm⁻³. Moreover, up to 10¹⁸ cm⁻³, J_SC and PCE remained almost consistent for PSC when Nb₂O₅ was ETL, later they tended to rise from 20.8 mA/cm² to 22 mA/cm² and from 15.3 to 16.5% (in magnitude), respectively, as opposed to other optimized devices with CdS, ZnSe and MZO combinations kept static throughout the period of increasing N_D of ETL. The higher value of N_D of ETL provides the assistance of charge extracting and carrying them out to the ETL/absorber layer. Contrarily, series resistances can the PV features low at a decreasing value of N_D^92,93. The same kind of trends were also attained in published findings⁹⁴. To find better-optimized results for each device, the optimal donor density of ETL was considered as 10¹⁸ cm⁻³ which was exactly the same as the initial value.

 Optimization of acceptor density of HTL

The illustration describes the effect of the acceptor density of HTL on the cell performance of Cs₂TiCl₆-based PSCs shown in Fig. 8b The variation of acceptor density (N_A) has been measured from the limit of 10¹⁴ cm⁻³ to 10²⁰ cm⁻³, concurrently holding the other performance parameters constant for all optimized devices.

While the N_A was increased, the V_OC was static for a while before initiating the steep rise to 1.2 V for all simulated combinations. On the subject of J_SC, each device has maintained a similar pattern of stability till 10¹⁴ cm⁻³ of acceptor density, then decreasing to 15.8 mA/cm² for PSC using Nb₂O₅ as ETL in contrast declined to 17.5 mA/cm² accounted to rest of structures. There had been a remarkable fluctuation curve witnessed for FF with respect to the increment of HTL N_A. At first, the FF decreased from 86 to 82% (in magnitude), then the FF curve commenced to burgeon dramatically and reached 89% at 10²⁰ cm⁻³ of HTL N_A. With the increase in N_A of HTL, the cell efficiency started collapsing up to 10¹⁷ cm⁻³ afterward the efficiency of CdS, ZnSe, and MZO-configured devices escalated to 18% compared to 16% when CdS was implemented as an ETL. As the V_OC recorded a swift rise along with the growing N_A of HTL that can be the objective of electric potential in between the intersection of HTL and perovskite absorber ⁹⁵. In contrast, the PCE and FF increased as the N_A of HTL expanding further facilitates the conductivity which has an astonishing impact on accumulating charges because of the upgraded electric field existing⁹⁶.

 Optimized J-V and Q-E characteristics

Fig. 9

a The current density–voltage (J-V) curve for the pristine optimized structure, b the current density–voltage (J-V) curve for the final optimized structure, c the Q-E curve of the pristine optimized structure and d the Q-E curve of the final optimized device.

From Table 1, it is evident that key parameters such as bandgap and electron affinity, which play critical roles in band alignment, are quite similar across the ETL materials studied. Other properties, including electron and hole mobilities, also show comparable values. This similarity in parameter values suggests that these ETL materials exhibit consistent behavior in device performance. A similar trend has also been observed in previous study¹³. The requirement of having fundamental knowledge about short circuit current density with respect to voltage is compelling when the SC gets stimulated. The changes in current density in connection with voltage for pristine and final optimization have been shown in Figs. 9a,b. As the voltage increased, the current densities remained unchanged and had been precipitously shrinking for all optimized structures at some point of increasing voltage. In Fig. 9a, it was observed that ZnSe as an ETL-related device showed J_SC of about 15 mA/cm² until the V_OC was ˃1.58 V; concurrently the J_SC was almost 20 mA/cm² for Nb₂O₅, MZO and CdS-associated structures at ˂0.9 V of Voltage. However, at the final stage, all different ETL-configured configurations except the device built with ZnSe prolonged their consistent trend of J_SC up to V_OC of less than 1.18 V on increasing voltage in the final optimization process. While the linked device had shortened the J_SC curve when V_OC was ˂0.88 V, the value of J_SC went up to 20 mA/cm². Exhibiting defect states in the absorber layer has a considerable impact on all PV features. The findings matched with previous literature that solid crystallinity impedes charge recombination but enhances performance⁹⁷. This observed 3% variation in performance ratio between the pristine and final optimized devices arises due to the complex interplay of factors beyond the basic J-V relationship. Specifically, while voltage and current density are interdependent, the optimization process alters several properties such as interface quality, defect density, and carrier dynamics. Improvements in these areas reduce recombination losses and enhance charge extraction, thereby slightly shifting the J–V characteristics and the fill factor, leading to the observed variation^98,99. Such changes reflect real physical improvements in device operation rather than inconsistencies.

On the other hand, the QE curve for the pristine and final optimized configurations was displayed in Figs. 9c,d by changing the wavelength ranging from 300 nm to 900 nm. The classification of QE is the ratio of all charge carriers produced by light to the number of photons that hit the solar cell¹⁰⁰. During the period of pristine optimization, all devices designed with various ETLs had almost half square-shaped QE curves and experienced almost 100% efficiency in the visible wavelength range of 360–560 nm. The CdS, ZnSe, and MZO-based devices had the taste the best QE of 99.7% when the wavelength was about 390 nm as opposed to 85% at 370 nm to Nb₂O₅-associated PSC. The poor performance of Nb₂O₅ in quantum efficiency (QE) can be attributed to its relatively lower carrier mobility and potential for forming defect states at the ETL/absorber interface, which increases charge carrier recombination. Additionally, the interfacial contact quality with Cs₂TiCl₆ may be suboptimal compared to the other ETLs, thereby impeding charge separation and transport.

 Effect of resistance and temperature

 Effect of series and shunt resistance

Figure 10a depicts the experimentation of the electrical performance of the series resistance of different PSC structures. In this experiment, series resistance (R_S) is fluctuated between 0$\:\:{\Omega\:}{\text{c}\text{m}}^{2}$ and 6 $\:{\Omega\:}{\text{c}\text{m}}^{2}$, keeping shunt resistance (R_Sh) fixed. When R_S of optimized cell device increases, there is a marginal rise in the V_OC from 1.164 V to 1.165 V for Nb₂O₅ -based SCs and from 1.167 V to 1.168 V for CdS, ZnSe and MZO-based PSC. However, increasing series resistance does not influence the J_SC of SCs. The Jsc is classified by the ratio of absorbing light by the device to the successful conversion of absorbed photons into electrical current. In SCs, R_S is caused by the resistance of each layer utilized and by the loss of charge transfer between the layer and metal contacts¹⁰¹. However, augmentation of R_S is considered the main factor for dropping the FF to 82% (in magnitude), and η downturned significantly to an average of 2% (in magnitude) for each SC device. The R_S is viable for impeding the current flow that leads to power destruction within a device and, eventually, costs the device’s overall performance. So, the best PCE is exhibited when a low series resistance exists.

Fig. 10

Significance of a Series resistance on V_OC (V), J_SC (mA cm⁻²), FF (%) and η (%) b Shunt resistance on V_OC (V), J_SC (mA cm⁻²), FF (%) and η (%). c Temperature on V_OC (V), J_SC (mA cm⁻²), FF (%) and η (%).

On the other hand, Fig. 10b shows the alternation of PV parameters along with the shunt resistance for four structures. The routes used for recombination are the cause of shunt resistance¹⁰². The efficiency of the PSCs is simulated in terms of varying the R_Sh from 10 $\:{\Omega\:}{\text{c}\text{m}}^{2}$ to 10⁷$\:\:{\Omega\:}{\text{c}\text{m}}^{2}$ when the R_S stationed constant at 0.5$\:\:{\Omega\:}{-\text{c}\text{m}}^{2}$. Throughout the upswing, R_Sh, the V_OC, and the J_SC proliferated exponentially to 10²$\:\:{\Omega\:}{-\text{c}\text{m}}^{2}$ R_Sh before remaining unchanged till 10⁷$\:\:{\Omega\:}-{\text{c}\text{m}}^{2}$ for all four optimized devices. On the contrary, between 10 $\:{\Omega\:}{-\text{c}\text{m}}^{2}$ to 10³$\:\:{\Omega\:}{-\text{c}\text{m}}^{2}$ R_Sh, the FF, and PCE accounted for a steady increase of 63% (in magnitude) and 15% on average (in magnitude), respectively which is well matched with previous experimental literature^103–105. After that, both of these continued. The enhancement of PCE is due to the elimination of leakage current which develops when there are some manufacturing defects or imperfections thus raising the R_Sh. A significant R_Sh lessens the obstruction stated in the p-n junction and permits more current to flow via it¹⁰⁶.

 Effect of temperature

The temperature T (K) has a great impact on the performance of PSCs while they are illuminated to sunlight in various geographical regions. So, it is considered an indispensable prerequisite to figuring out the temperature-subordinated electrical parameters for PSC are shown in Fig. 10(c). In this study, four different structures are simulated varying the temperature from 275 K to 450 K. For each device, the FF decreased from 90 to 83% and the V_OC reduced by 30% in voltage respectively with respect to heated temperature. As regards the J_SC, there was an upward trend observed for PSC with Nb₂O₅-based PSC due to band gap reduction of material thus more charge pairs will be produced¹⁰⁷. While the remaining three devices showed stable voltage during that period. Different declinations of cell efficiency have been recorded for all four optimized devices. When the temperature maximized to 450 K, the efficiency of Nb₂O₅-based SCs curtailed slowly to 13% when CdS, ZnSe, and MZO-based PSCs followed a similar diminution of cell efficiency promptly to 13%. The reason for deteriorating efficiency can be the stress and deformation are proportioned with temperature increases, therefore, intensifying interfacial defects, causing inadequate internal conduction between layers, and recombination increases as well¹⁰⁸. Furthermore, the augmentation of temperature is authoritative to the reduction diffusion length (L) which in turn is series resistance, resulting in reduced efficiency¹⁰⁹. The consistent shrinking of device performance along with rising temperature has been acquired in previous research findings⁵⁶.

 Analysis of generation and recombination rate

The investigation of the influence of generation rate for initial and final optimization has been carried out and demonstrated in Figs. 11a,b along with the changeable position in the device. The transition of excited electrons from the VB to the CB generates the electron-hole pairs, leaving a hole in the VB layer during the carrier production stage which is defined by the release of electrons and holes. For initial optimization in Fig. 11a, the generation rate for all structured devices was 2.5 × 10²¹ cm³s⁻¹ at 1.2 μm position. That ratio remained unchanged but positioned at 0.8 μm for the final optimization process that was depicted in Fig. 11b. The highest number of electrons produced at that region where the majority of photons are absorbed instigated a significant generation rate in the device. The generation of electron-hole pairs, G (λ, x), can be calculated by SCAPS-1D in terms of the incident photon flux, N_phot (λ, x) for each spectrum and region:

$$\:G\:(\lambda\:,\:x)\:=\:\alpha\:\:(\lambda\:\:,\:x).\:Nphot\:(\lambda\:,\:x)\:$$

Fig. 11

Effect of a Generation rate for the initial optimized structure, b Generation rate for the final optimized structure, c Recombination rate for the initial optimized structure, d Recombination rate for the final optimized structure.

In contrast, the recombination rate is considered as opposite of the generation rate, involving joining and separating the electrons and holes within the CB. The rate of recombination in perovskite is affected by both the lifetime and density of the charge carrier. Moreover, the imperfection state at each perovskite layer plays a vital impact in electron-hole recombination. During the initial optimization Fig. 11c the recombination rate was almost 1 × 10¹⁹ cm³s⁻¹ for all optimized structures Fig. 11d within the range of 0.2 μm to 1.2 μm where CdS showed comparatively the highest recombination. The reason for that maximum rate is more electrons located in the conduction band outstepped the band energy gap and placed into the VB and replaced of place of hole at that limit. Consequently, the electron-hole recombination was affected by energy levels generated at that peak position. Un-even distribution of recombination rates occurs due to the grain boundaries and defects ¹¹⁰.

The quantum efficiency (QE) of the devices shows characteristic variation with wavelength. At shorter wavelengths (300–550 nm), the QE is relatively high due to strong absorption near the surface of the absorber, where the photogenerated carriers are effectively collected before recombination. In the longer wavelength range (550–800 nm), the QE gradually decreases because photons penetrate deeper into the device, increasing the likelihood of carrier recombination before collection. The differences in QE among devices using various ETLs arise from differences in conduction band alignment and interface quality, which directly affect carrier extraction. For instance, better band alignment at the ETL/absorber interface leads to improved charge transport and higher QE, whereas poor interface quality or unfavorable band offsets enhance recombination losses, especially for long-wavelength photons

 Comparison of SCAPS-1D results with previous work

Table 4 The comparison of PV constraints of Cs₂TiCl₆-based PSCs.

The latest experimental and theoretical findings on Cs₂TiCl₆-based PSCs are comparatively analyzed with our study and shown in Table 4. The optimized Cs₂TiCl₆-based PSC presents a higher PCE compared to the previously used device structure with a similar kind of halide perovskite absorber. The device structures had a desired PCE are 15% while previously device configurations like FTO/TiO₂/Cs₂TiCl₆/CuSCN/Ag obtained 5.5% of PCE. In comparison with other Cs₂TiCl₆-based PSCs, the present solar structure has displayed higher J_SC and FF values. The executed ETLs and HTLs in that study may not be well matched with those used in prior conducted experimental investigations, which is considered a possible reason for the discrepancy. What is more, the difference in optical properties depends on the variation of absorbers, consequently influencing the absorption of SC energy. It is observed that ETL discloses outstanding PV performance according to JV and QE characteristics in that present study; the reason is to display better band alignment as compared to other studied ETLs. The carrier transportability and transparency ETL play a significant role in the device’s efficiency of extracting out and conveying charge. The CdS is ubiquitously used as an ETL in PSC configurations due to lower hysteresis factors and higher electron mobility in comparison to TiO₂; the latter is responsible for higher extraction rates, so as device performance¹¹³. In addition, exceptional transparency shown by CdS acts as a vital element for amplifying the light absorption within the perovskite absorber layer¹¹⁴.

 Conclusion

A stable, lead-free, eco-friendly, and fully inorganic perovskite solar cell (PSC) based on Cs₂TiCl₆was analyzed and simulated using SCAPS-1D, where Cs₂TiCl₆ served as the light-absorbing layer. Throughout the investigation, a diverse set of hole transport layers (HTLs) and electron transport layers (ETLs) were examined to identify the most efficient device configuration. Key findings are listed below:

• 1. Among the various candidates, the combination of CdS, Nb₂O₅, ZnSe, and MZO as ETL, paired with a CdTe HTL, demonstrated superior performance compared to other HTL/ETL combinations.

• 2. Initial optimization revealed that these four devices were suitable for further analysis regarding absorber characteristics, HTL thickness, donor and defect densities in the ETL, acceptor and defect densities in the HTL, series resistance (R_S), shunt resistance (R_sh), temperature effects, generation rate, recombination rate, J–V characteristics, and quantum efficiency (QE).

• 3. Notably, the CdS-based device achieved an efficiency of 14.3% after optimizing the absorber thickness, and an enhanced efficiency of 18% after optimizing the HTL thickness. The findings indicate that minimizing series resistance and maximizing shunt resistance are crucial strategies to achieve the highest possible device performance.

• 4. Temperature effects were also evaluated, and the maximum efficiency was observed at 300 K. Following final optimization, the ZnSe-based device exhibited superior J–V performance under specific voltage conditions.

• 5. The CdS- and MZO-based PSCs displayed distinctive J–V, and QE behavior, while the Nb₂O₅-based device showed the poorest QE performance across the visible spectrum.

• 6. Based on the results, the optimal device structure proposed is FTO/CdS/Cs₂TiCl₆/CdTe/Au, achieving a power conversion efficiency (PCE) of 18.15%, a short-circuit current density (_Jsc) of 17.83 mA/cm², an open-circuit voltage (V_OC) of 1.188 V, a fill factor (FF) of 89.51%, and a quantum efficiency (QE) of 99.7% in the visible region.

Overall, this comprehensive study offers valuable insights that will assist in the future design and development of lead-free, environmentally friendly Cs₂TiCl₆-based perovskite solar cells.