Interface engineering and defect passivation for enhanced hole extraction, ion migration, and optimal charge dynamics in both lead-based and lead-free perovskite solar cells

The study elucidates the potential benefits of incorporating a BiI3 interfacial layer into perovskite solar cells (PSCs). Using MAPbI3 and MAGeI3 as active layers, complemented by the robust TiO2 and Spiro-OMeTAD as the charge-transport-layers, we employed the SCAPS-1D simulation tool for our investigations. Remarkably, the introduction of the BiI3 layer at the perovskite-HTL interface significantly enhanced hole extraction and effectively passivated defects. This approach minimized charge recombination and ion migration towards opposite electrodes, thus elevating device performance relative to conventional configurations. The efficiency witnessed a rise from 19.28 to 20.30% for MAPbI3 and from 11.90 to 15.57% for MAGeI3. Additionally, MAGeI3 based PSCs saw an improved fill-factor from 50.36 to 62.85%, and a better Jsc from 13.22 to 14.2 mA/cm2, signifying reduced recombination and improved charge extraction. The FF for MAPbI3 based PSCs saw a minor decline, while the Voc slightly ascended from 1.24 to 1.25 V and Jsc from 20.01 to 21.6 mA/cm2. A thorough evaluation of layer thickness, doping, and temperature further highlighted the critical role of the BiI3 layer for both perovskite variants. Our examination of bandgap alignments in devices with the BiI3 interfacial layer also offers valuable understanding into the mechanisms fueling the observed improvements.

In recent years, perovskite solar cells have made significant improvements in achieving power conversion efficiencies (PCE) to a peak of 25.7% 1 .The perovskite has emerged as a promising option in photovoltaic (PV) technologies owing to its exceptional light absorption characteristics [2][3][4][5] .The general formula for perovskite is ABX 3 , where "A" represents an organic/inorganic cation such as methylammonium (CH 3 NH 3 + , MA + ) 6 or formamidinium (NH = CHNH 3 + , FA + ) 7 , the element "B" is characterized by the presence of metal cation such as lead (Pb 2+ ), germanium (Ge 2+ ) or tin (Sn 2+ ) and "X" represents a halogen ion such as I − , Br − , or Cl − .The exceptional efficiency of solar cells utilizing three-dimensional ABX 3 perovskite can be attributed to several key factors.These factors include their ability to absorb light across the visible to near-infrared spectrum, their minimal exciton binding energy (approximately 2 meV), direct band gap [8][9][10][11] , a large diffusion length, and high charge particle movement capability.These qualities make them highly favored as ideal photovoltaic materials 12 .Furthermore, reducing the defect density in perovskite films through various techniques has the potential to enhance photovoltaic performance, consequently increasing efficiency 13 .The unique characteristics of PSC position them as a compelling candidate for exploration within the domain of photovoltaic cells, among them the methyl ammonium lead tri-iodide (CH 3 NH 3 PbI 3 /MAPbI 3 ) variant of PSC being particularly prevalent.

Literature review
In the pursuit of advancing PSC technology, researchers have used various innovative interface engineering strategies to enhance both efficiency and stability.One significant breakthrough was achieved by Min et al., who developed PSCs with atomically coherent interlayers on SnO 2 electrodes.This approach not only minimized interfacial defects but also optimized charge extraction and transport mechanisms.The result was a remarkable increase in PCE to 25.8%.By addressing the issue of interfacial defects, this study not only increased the PCE but also shed light on the critical role of electrode interlayer coherence in the operational stability and efficiency of PSCs 40 .In another study Zhang et al. introduced another layer of passivation by integrating bifunctional alkyl chain barriers at the crucial junction between perovskite and HTL.This effectively blocked electron recombination and protected the cells against moisture, leading to substantial increase in both efficiency and stability.The alkyl chain barriers represent a dual-function solution that not only enhances the electrical performance of PSCs but also addresses environmental durability, a key challenge for the commercial viability of perovskite-based photovoltaics 41 .Further exploring the potential of interface engineering, Dong et al. created interpenetrating interfaces between the perovskite layer and electron-transporting materials.This led to PSCs achieving efficiencies up to 22.2%, with significant improvements in operational stability and mechanical robustness.The addition of the interface layer highlights the importance of smooth connection between different layers in PSCs, ensuring efficient charge transport and reducing the risk of mechanical failure under operational stresses 42 .In another Chen et al. focused on the in situ formation of 2D perovskite layers at the interface of mixed perovskites and CuSCN.This method led to an increase in PCE from 13.72 to 16.75% while simultaneously improving moisture and photostability.The use of 2D perovskites as interface engineering layers highlights the versatile potential of these materials in enhancing both the efficiency and durability of PSCs, addressing two of the most critical challenges in the field 43  www.nature.com/scientificreports/as an interface engineering layer, which enhanced the PCE from 15.17 to 18.56% and improved the stability of PSCs.This approach underscores the potential of quantum dot technologies in fine-tuning the optical and electrical properties of PSCs, offering a pathway to simultaneously achieve high efficiency and stability 44 49 .
Moving towards Bismuth materials, the study introduced Bismuth Telluride (Bi 2 Te 3 ) nanoplates as an interlayer in all-inorganic PSCs, enhancing efficiency and stability.This interlayer, positioned between the CsPbBrI 2 absorber layer and the Spiro-OMeTAD HTL, significantly reduced trap states and charge recombination.The optimized use of Bi2Te 3 interlayer led to PCE increase from 7.46 to 11.96% and maintained over 70% of its initial PCE after 50 days without additional encapsulation, demonstrating an effective approach to improving PSC performance 41 .In another study, the incorporation of a BiI 3 passivation layer between the compact TiO 2 ETL and the perovskite absorber significantly enhances the efficiency and stability of planar perovskite solar cells.This interface engineering approach resulted in an increase in PCE from 13.85 to 16.15%, with a peak efficiency of 17.79%.The application of the BiI 3 layer effectively facilitates electron extraction and minimizes hysteresis, marking a pivotal advancement in the performance optimization of perovskite solar cells 40 .Each of these studies collectively underscores the transformative impact of interface engineering on the development of PSCs and is summarized in Table 1.By optimizing the interfaces between various layers within PSCs, researchers have not only achieved significant efficiency and stability but also provided a roadmap for overcoming some of the most persistent challenges in the field of photovoltaic.
Building on the foundation laid by different research in the field of PSC technology, the present study distinguishes itself through a focused investigation into the effects of a BiI 3 interlayer on the performance of PSCs.Unlike other studies that have broadly explored interface engineering with various materials, this work focuses on the specific application of BiI 3 ILs, providing a new insight in the optimization of PSC interfaces.This research differs from other work by applying a dual-focus approach of examining the performance enhancements in PSCs with two distinct absorber materials when integrated with a BiI 3 IL.This study shifts away from the traditional focus on conventional materials such as SnO 2 , alkyl chain barriers, and quantum dots, which have been extensively explored for their roles in improving charge transport and addressing defects at interfaces.The targeted exploration of the BiI 3 role as a passivation layer not only bridges a gap in the existing literature but also unveils a novel pathway for increasing the PSC efficiency through strategic interface modification.

Device methodology
There are several numerical modeling software options accessible to facilitate the computational analysis of photovoltaic cell performance, including SETFOS, SCAPS, SILVACO, COMSOL, and ATLAS [50][51][52][53] .The choice of employing SCAPS-1D version 3.3.10 is driven by its beneficial attributes.These features include its open source nature, an intuitive interface that is easy to use and control, the capacity to simulate scenarios with or without light, and the capability to design a heterostructure-based system with up to seven layers 50,54,55 .The SCAPS-1D software is capable of assessing the effectiveness of photovoltaic through estimation of multiple parameters, such as PCE, FF, V oc , J sc , energy band, and IV Curve characteristics.SCAPS-1D is based on solving the basic semiconductor equations that govern the operation of photovoltaic devices 56 .These equations include the Poisson's Equation (Eq.1), Continuity Equations (Eq.2), Current Density Equations (Eq. 3) and Generation/Recombination (Eq.4).The Poisson's Equation is a fundamental principle in electromagnetism and semiconductor physics, expressing the relationship between the electric potential in a region and the charge density within that region.It helps determine the electric field distribution across the semiconductor layers.The equation accounts for the static charge present and is crucial for understanding how electric fields form in response to charged defects, dopants, and the separation of electrons and holes within the device structure.While the Continuity Equations in semiconductor physics ensure the conservation of charge, describing how electron and hole densities change over time due to generation, recombination, and the flow of these carriers within the material.These equations are vital for predicting the dynamic behavior of charge carriers in response to external stimuli, such as light absorption in photovoltaic cells, and are essential for analyzing current flow and the effects of carrier recombination and generation on device performance.Similarly, the Current Density Equations describe how electrical current flows through a semiconductor material due to both the drift of charge carriers in an electric field and their diffusion from regions of high concentration to low concentration.These equations are key to modeling the transport of electrons and holes in photovoltaic devices, enabling the calculation of current-voltage characteristics under various conditions.They highlight the dual nature of charge transport, incorporating the effects of the material's electric field and the carriers' thermal energy.Finally, the Generation/Recombination mechanisms show the processes by which charge carriers (electrons and holes) are created and finish within a semiconductor.Generation can occur through thermal energy or by absorbing photons, while recombination happens when electrons and holes combine, releasing energy.These mechanisms significantly impact the efficiency of photovoltaic devices, as they determine the net charge carrier density available for electrical current production.Understanding these mechanism is crucial for designing materials and device structures that minimize recombination losses and maximize generation for improved solar cell performance.
where ∇ 2 is the Laplacian operator, ϕ is the electric potential, ρ is the charge density, ε is the permittivity, c represent the electron (n) and hole densities (p), J c are the current densities for electrons and holes, G is the rate of generation of carriers, R is the rate of recombination, q is the elementary charge, μ c is the mobilities of electrons and holes, D c is the diffusion coefficients for electrons and holes, ∇c is gradients of electron and hole densities, n i is the intrinsic carrier density, τ n and τ p are the electron and hole lifetimes, and n 1 and p 1 are the electron and hole densities at thermal equilibrium, respectively.
Modeling the device in detail is a crucial step towards highlighting the impact of the IL on device functioning.It is intended to aid experimentalists in modifying their studies 57 .The simulations were conducted under standard testing conditions (STC) with a light intensity equivalent to AM 1.5 spectrums (1000 W/m 2 ) and a temperature of 300 K.It is important to highlight that the simulations did not consider parasitic resistances.We have modeled four unique PSC structures, each utilizing ETL of TiO 2 and HTL of Spiro-OMeTAD.Two of these structures employ MAPbI 3 as the absorber layer.The remaining two structures utilize MAGeI 3 as the absorber.One PSC from each absorber is modelled with the IL (Fig. 1b) while the other structure is without the IL (Fig. 1a). Figure 2 shows the energy level of the different materials used in this study.When exposed to light, photons impact the ETL and then disperse towards the HTL side.When photons are absorbed by the perovskite material, charge carriers are generated within the layer, which then migrate into the layers responsible for transporting electrons and holes.The optimized dimension of absorber layer, ETL, HTL, IL, along with various factor such as electron-hole mobility, effective density of states, doping densities, defect densities, and electron affinities have been collected from literature, which are comprehensively listed in Table 2 [58][59][60] .This methodology allows us to systematically analyze the effects of incorporating an interface layer across different perovskite absorber materials. (1)

Effect of passivation layer on PSC energy band alignment
The performance of PSCs is significantly influenced by the energy band alignment between the PSC and the CTLs.For efficient electron extraction from the perovskite material, the conduction band (CB) of the ETL and the CB of the PSC must align with minimal offset.To block the holes their valence bands (VB) should show a considerable difference.If the VBs are too close, there is a risk that holes might migrate towards the ETL, leading to recombination.Proper alignment between the VB of the HTL and the perovskite material is crucial for facilitating hole separation.Similarly, a significant offset in their CBs is essential.If the CBs are aligned too closely, electrons may migrate towards the HTL, again leading to recombination.The characterization of ideal band alignment in PSCs requires a minimal offset at the CB and a maximal offset at the VB between the perovskite and the ETL.The aim is to enable a smooth flow of electrons from the active layer to the ETL while simultaneously blocking hole transmission 61 .Likewise, the minimal valence band offset (VBO) and maximal conduction band offset (CBO) are crucial characteristics for both the HTL and perovskite material, facilitating seamless hole transmission from the absorber to the HTL while hindering electron mobility.
The engineering of an IL between the absorber and the HTL is a widely recognized approach for effectively mitigating defects, typically enhancing hole extraction by impeding the movement of secondary electrons 21 .Figure 3 shows the energy band alignment of the PSCs while Table 3 shows the VBO and CBO formed by the  www.nature.com/scientificreports/layers.The VBO and CBO have been calculated from the electron affinity (χ) and band gap (Eg) of the material using the formula: The introduction of an IL has been observed to adjust the alignment of energy levels among the films and prevent ion migration.The rate of hole injection, especially between the active layer and the HTL, is influenced  by the alignment of the interface energy levels.The presence of an energy barrier at the interfaces leads to charge carrier recombination and thus limits the efficiency of charge transfer.Conversely, the absence of an EB across the interface facilitates efficient charge transfer and injection, reducing recombination rates.The incorporation of a BiI 3 IL at the junction between the absorber and the HTL enhances hole transport across the interface and may help mitigate interface charge recombination.
In the context of the MAPbI 3 /TiO 2 interface, as delineated in Table 2, a CBO of − 0.1 eV and a VBO of 1.75 eV facilitate efficient the transport of charge from MAPbI 3 to the TiO 2 .The small CBO facilitates electron flow, while the substantial positive VBO impedes hole migration into the TiO 2 layer, thereby minimizing electron-hole recombination at this juncture.
At the absorber/HTL interface, with a CBO of 1.7 eV and a VBO of − 0.25 eV, there is a promotion of efficient hole transport from MAPbI 3 to Spiro-OMeTAD due to the small VBO and large CBO.The large CBO serves as an electron-blocking layer, preventing electrons from reaching the Spiro-OMeTAD layer thereby lowering the likelihood of recombination.
Introduction of the BiI 3 interfacial layer between the active layer and HTL provides a climbing ladder for the holes to the HTL.The IL forms a CBO of − 0.2 eV and a VBO of 0.37 eV at the MAPbI 3 /BiI 3 interface.The VBO of 0.37 forms a spike which increases the electric potential at the heterojunction than the MAPbI 3 /HTL hetero junction which forms a cliff.The higher electric potential efficiently transfers holes from MAPbI 3 to BiI 3 , reducing the likelihood of hole recombination.At the Spiro-OMeTAD/BiI 3 interface, the CBO of 1.9 eV produces a larger barrier for the electrons.
Similarly, at the MAGeI 3 /TiO 2 interface, a CBO of − 0.02 eV and a VBO of 1.32 eV support the efficient electron transport from MAGeI 3 to TiO 2 .The small CBO of MAGeI 3 with TiO 2 , along with a large positive VBO, promotes the flow of electrons while restricting hole migration to TiO 2 , thus reducing recombination at this interface.
At the MAGeI 3 /HTL interface, a CBO of 1.78 eV and a VBO of − 0.68 eV is formed.The large CBO blocks electrons to the HTL.However, the large negative VBO forms a cliff which not only blocks some holes but also reduces the built-in potential.Upon introducing a BiI 3 interface layer between MAGeI 3 and Spiro-OMeTAD, the energy level alignment features a CBO of − 0.12 eV and a VBO of − 0.06 eV.The small VBO forms a ladder for the holes to climb to reach the HTL.Furthermore, the significantly small cliff causes a higher electric potential at the hetero junction which improves hole transportation.
In conclusion, the strategic introduction of a BiI 3 IL has demonstrated a tangible impact on the charge transport dynamics within perovskite solar cells.By fine-tuning the energy level alignment across the interfaces, the BiI 3 IL optimizes the transport of charge carriers for both perovskites.The IL not only facilitates as a ladder for holes towards the HTL but also increases the electric potential at the interface.

IV characteristics
Comprehensive IV characteristics derived from the four structuresare are shown in Fig. 4. The TiO 2 /MAPbI 3 / Spiro-OMeTAD exhibited a PCE of 19.28%, J sc of 20.01 mA/cm 2 , FF of 77.58%, and a V oc of 1.24 V. Similarly, in the case of TiO 2 /MAGeI 3 /Spiro-OMeTAD configuration, the simulated device demonstrated a V oc of 1.7 V, a J sc of 13.22 mA/cm 2 , a FF of 50.36%, and a PCE of 11.90%.The structures were then analyzed with the passivation layer.Remarkably, the introduction of this BiI 3 interface led to a notable enhancement in key photovoltaic parameters.In MAPbI 3 , the V oc observed a shift from 1.24 to 1.25 V. Concurrently, the J sc displayed an improvement, transitioning from 20.01 to 21.6 mA/cm 2 .These increments culminated in the rise of the overall PCE from 19.28 to 20.30%.These enhancements contributed to an overall PCE increase from 19.28 to 20.30%.This improved performance is because of the favorable band alignment facilitated by the BiI 3 interlayer, which optimizes charge carrier separation and extraction, as depicted in Fig. 3.The optimized band alignment reduces charge carrier recombination at the interface and promotes more efficient charge transport and extraction, crucial for achieving higher PCE.
Similar to this, by the introduction of BiI 3 interface between the MAGeI 3 absorber and Spiro-OMeTAD HTL the V oc remained invariant at 1.7 V. Yet, J sc witnessed an increased from 13.22 to 14.2 mA/cm 2 .The FF increased significantly from 50.36 to 62.85%.Consequently, the PCE jumped from 11.90 to 15.57% with BiI 3 integration.The enhancement in J sc and FF, and thereby the PCE, is directly linked to the advantageous band alignment introduced by the BiI 3 layer.This alignment reduces charge carrier recombination and improves interfacial impedance, facilitating more efficient charge transport across the interfaces.The presence of the BiI 3 layer acts as a bridge, enhancing charge flow between the absorber and HTL, which is critical for the efficient extraction of photo-generated carriers.These results show the important role of interface engineering, particularly through the integration of passivation layers like BiI 3 , in enhancing the photovoltaic performance of PSCs.By optimizing the interfacial properties and band alignment, significant improvements in key performance parameters such as J sc , FF, and PCE can be achieved, paving the way for the development of more efficient and stable PSCs.
Table 4 compares the results of this study with fabricated experimental data of MAPbI 3 PSC using interface layers.When Thiophene and Pyridine are used as the passivation layer in the PSC the PCE of the cells increase from 13 to 15.3% and 16.5%, respectively.This improvement is attributed to the passivation of under-coordinated Pb ions within the perovskite crystal.Similarly, when Tetrafluoro-tetracyanoquinodimethane (F4TCNQ) is used as the interface layer the PCE increases from 14.3 to 16.4% and improved long-term stability in ambient air.When the Bismuth based layer of Bi 2 Te 3 is used as the passivation layer, the PCE increases from 7.46 to 11.96% and maintained over 70% of its initial PCE after 50 days without additional encapsulation.Lastly, the integration of a BiI 3 passivation layer, the PCE increases from 13.85 to 16.15%, highlighting the layer's effectiveness in facilitating electron extraction and minimizing hysteresis.Similarly in our work when the BiI 3 is used as the passivation layer, the PCE of MAPbI 3 increases by 1.02% while for MAGeI 3 it increases by 4.63%.The simulation models produce results that align closely with the experimentally fabricated data, underscoring the predictive accuracy and relevance of our computational approach in mirroring real-world PSC performance enhancements.

Impact of absorber layer thickness on photovoltaic parameters
The thickness of the active layer plays a critical role in affecting the optical properties, morphology, and overall performance of PSC 62,63 .Figure 5 shows the effect of absorber thickness on the PSCs.Increasing the thickness of both MAPbI 3 and MAGeI 3 layers influences the device performance, particularly when a BiI 3 interfacial layer is introduced.It's observed that for both types of structures, the J sc rises as the layer thickness increases, due to enhanced light absorption capabilities 64,65 .Larger thickness leads to absorption of more photons, especially those of higher wavelength.These photons contribute to more photogeneration of charge carriers which leads to higher J sc .Specifically, for the MAPbI 3 and MAGeI 3 with the BiI 3 IL consistently outperform their counterparts in terms of J sc .The improvement is attributed to the BiI 3 layer acting as a passivation interface, which facilitates efficient charge extraction and reduces non-radiative recombination losses 66 .
For MAPbI 3 devices equipped with a BiI 3 interlayer, an initial decline in the V oc is observed as the layer thickness increased, which then stabilized.This behavior is attributed to the initial reduction in charge carrier recombination rates facilitated by the BiI 3 layer.The BiI 3 layer acts as a barrier, impeding non-radiative recombination pathways at the interface, which initially lowers V oc due to the adjustment phase of charge carriers to the new interface dynamics.As the thickness increases, the effect of the BiI 3 layer in reducing recombination becomes more prominent, leading to stabilization of V oc .The reduction in charge recombination is a critical factor in stabilizing V oc , as it allows for more efficient charge separation and extraction, ultimately enhancing device performance.Conversely, in the absence of a BiI 3 interlayer, MAPbI 3 devices exhibited fluctuating V oc values with a general decline at greater thicknesses.This decline is directly linked to increased trap-assisted recombination.Without the passivating effect of the BiI 3 layer, charge carriers are more susceptible to recombination through defect states within the perovskite layer, exacerbated as the layer thickness increases, leading to a decrease in V oc .For devices based on MAGeI 3 with a BiI 3 interlayer, a significant improvement in V oc was observed with increasing thickness.This improvement is due to the enhanced energy band alignment between the HTL, the BiI 3 interface, and the absorber layers.The optimized band alignment facilitates more effective charge separation and minimizes recombination losses, directly contributing to the observed increase in V oc .In contrast, without the BiI 3 interlayer, the V oc for MAGeI 3 devices decreased with increased thickness, which is attributed to enhanced bulk recombination, diminishing the quasi-Fermi level separation and thereby reducing the device's overall efficiency.
The FF trends for both MAPbI 3 and MAGeI 3 solar cells, irrespective of the presence of a BiI 3 interlayer, showed a decreasing pattern with increasing layer thickness.This phenomenon is attributed to increased bulk recombination and the accompanying resistive challenges that rise in series resistance with thicker layers.In the specific case of MAPbI 3 , the initial presence of a higher FF upon the introduction of a BiI 3 interlayer is linked to a higher VBO, which stabilizes at higher thickness, showcasing the BiI 3 layer's role in mitigating recombination and stabilizing device performance 67 .
The PCE trends observed for both MAPbI 3 and MAGeI 3 solar cells further underscore the pivotal role of the BiI 3 interlayer.The enhanced PCE in MAPbI 3 devices with BiI 3 is a direct result of improved photovoltaic parameters, such as J sc and V oc , which are in line with the previously discussed V oc and FF observations 63 .The increase in PCE with layer thickness in both cell types is attributed to improved light absorption and charge generation within the thicker perovskite layers.However, the MAGeI 3 devices with BiI 3 consistently exhibit superior performance, benefiting from the synergistic improvements in FF, J sc , and V oc .These improvements are indicative of the BiI 3 interlayer's efficacy in optimizing charge transfer dynamics and enhancing overall PV cell performance, thereby offering a comprehensive understanding of the physical mechanisms at play 66 .

Impact of absorber layer doping on photovoltaic parameter
In perovskite solar cells, the absorber layer plays a critical role in light absorption and charge generation 68,69 .The strategic introduction of n-type or p-type dopants, a process known as doping, serves to enhance the cells' photovoltaic efficiency by fine-tuning charge transport and carrier density, thereby optimizing device performance 70 .Figure 6 shows the impact of doping concentrations within the absorber layer on PSC performance, showcasing that both MAPbI 3 and MAGeI 3 cells exhibit variable J sc levels in response to altered doping levels 71 .Notably, MAPbI 3 cells equipped with a BiI 3 interface layer consistently surpass their counterparts, particularly when doping concentrations are optimized, a trend also observable in MAGeI 3 cells.Excessive doping, however, can induce increased recombination rates and diminish J sc , though the presence of BiI 3 effectively mitigates these negative effects by preserving elevated J sc values.
Further analysis reveals the effects of doping variations on the V oc for both MAPbI 3 and MAGeI 3 configurations, with and without a BiI 3 interface layer.Initially, MAPbI 3 cells lacking a BiI 3 layer exhibited slightly enhanced V oc within a lower doping range (E9-E14 cm −3 ) due to reduced parasitic resistance.Beyond this range, V oc values for MAPbI 3 cells with a BiI 3 layer began to exceed those without, attributed to the BiI 3 layer's passivation effects, which curtail recombination losses at higher doping levels (E15-E17 cm −3 ).This upward trend in V oc , facilitated by the BiI 3 interface, persisted across further doping levels, underscoring the layer's critical role in harmonizing charge extraction and recombination loss mitigation.In contrast, MAGeI 3 cells initially favored configurations without BiI 3 , yet V oc remained relatively constant across a broad doping spectrum (E9-E18 cm −3 ) for both setups, suggesting suboptimal doping levels.A significant shift was observed at higher doping levels, where MAGeI 3 cells without BiI 3 experienced a notable drop in V oc , whereas those with BiI 3 saw a substantial increase, highlighting the interface layer's effectiveness in reducing recombination losses and enhancing charge extraction.
The FF dependence on doping variation was also scrutinized for both MAPbI 3 and MAGeI 3 cells, revealing that the absence of BiI 3 initially resulted in a higher FF for MAPbI 3 cells, a phenomenon linked to increased series resistance with the BiI 3 layer.As doping increased, FF remained relatively stable for both cell types until the optimal doping level of E14-E15 cm −3 was reached, beyond which the FF of MAPbI 3 cells without BiI 3 continued to rise, albeit more modestly compared to those with the BiI 3 layer, which benefited from diminished recombination losses at elevated doping levels.MAGeI 3 cells exhibited stable FF up to E18 cm −3 , after which those without BiI 3 suffered a significant FF decrease, in contrast to the less severe reduction observed in cells with BiI 3 , emphasizing the layer's role in improving charge transport and minimizing series resistance at optimized doping levels.
The PCE trends also reflect the relation between doping levels and the presence of a BiI 3 interface layer.Initially, MAPbI 3 cells without BiI 3 showcased higher PCE values due to reduced parasitic resistance.However, a dramatic shift was noted at higher doping levels (E14 cm −3 and E17 cm −3 ), where the PCE of MAPbI 3 cells with BiI 3 surged, benefiting from synergistic improvements in V oc , FF, and reduced recombination losses, thereby outperforming those without the interface layer.Similarly, MAGeI 3 cells initially exhibited higher PCE without BiI 3 , but this advantage dwindled at elevated doping levels, where the presence of BiI 3 either stabilized or slightly increased PCE, attributed to enhanced charge extraction and minimized recombination losses.These observations highlight the critical importance of doping optimization and the integration of a passivation interface layer for advancing the efficiency and stability of PSCs, especially at higher doping concentrations.

Effect of temperature variation on PSC
In the quest for enhanced efficiency and thermal stability in perovskite solar cells, this study delves into simulations comparing the performance of these cells with and without interface layers, elucidating the implications of temperature on each parameter.Temperature has a notable influence on how well solar cells function 11,72 .Most PV cells achieve their highest efficiency when operating at around room temperature, which is about 300 K. To study how temperature affects the performance of PSC, the temperature varied across the range of 300-450 K for all the structures and the results are presented in Fig. 7.The efficiency of PV cells declines with an increase in temperature.Crystalline silicon cells, a temperature coefficient ranging from − 0.3 to − 0.5%/°C is usual 73 .This means that for each degree Celsius rise in temperature, the efficiency of the solar cell decreases by that percentage.The fundamental physics underlying the temperature effect on PSCs begins with the thermal dependency of the semiconductor bandgap.As temperature increases, the bandgap of the semiconductor material narrows due to the increased vibrational energy of the lattice 74 .This reduction in bandgap energy directly leads to a decrease in V oc , as the potential difference that can be generated by the solar cell is diminished.The narrowing bandgap reduces the energy barrier for charge carrier recombination, thereby increasing non-radiative recombination rates and further decreasing V oc .Furthermore, the increase in temperature also leads to an increase in the intrinsic carrier concentration, which further reduces the open-circuit voltage.The Perovskite solar cells, which have gained attention due to their impressive lab-scale efficiencies, demonstrate a complex relationship with temperature, often degrading faster at elevated temperatures 75 .Some perovskite structures undergo phase transitions when subjected to elevated temperatures, such as the shift from tetragonal to cubic phases in organic-inorganic lead halide perovskites 76 .This can lead to a change in their optical and electronic properties 77 .For instance, phase changes can affect the material's absorbance and its electronic band structure, potentially degrading the cell's efficiency and thermal stability.One of the key concerns with perovskite materials is their thermal stability.Prolonged exposure to high temperatures can lead to degradation of the material, significantly reducing its efficiency and lifespan 78 .Temperature variation significantly affects the performance of perovskite-based solar cells.An increase in temperature can cause a decline in open-circuit voltage and fill factor, leading to a reduction in overall efficiency 79 .Increased temperature also impacts both the bandgap energy and the material's conductivity within the cell, leading to a decline in its overall performance 80 .
Analyzing V oc variations in Fig. 7, MAPbI 3 systems displayed a consistent decline with increasing temperature, both in the presence and absence of the BiI 3 interface layer.The reduction in V oc can be scientifically rationalized by the increased non-radiative recombination rates at higher temperatures.The energy difference between the Fermi levels of the electron and HTL might reduce, leading to a decrease in V oc .For MAGeI 3 systems without the interface, a similar decline in V oc was noted with rising temperature, potentially for the same reason.However, when paired with the BiI 3 interface layer, MAGeI 3 devices exhibited a more pronounced V oc drop.In the context of J sc , it was observed that as temperature escalated, MAPbI 3 devices, regardless of the presence of the BiI 3 interface layer, showed negligible variations.This can be attributed to the fact that J sc is predominantly dependent on the number of photo-generated carriers, and in the MAPbI 3 system, temperature elevation might not substantially affect this number or the carrier collection efficiency.Similarly, in MAGeI 3 -based systems, both with and without the interface layer, J sc remained relatively unaltered with temperature changes.This indicates that the intrinsic properties and electronic pathways of MAGEI 3 might be relatively resistant to temperature perturbations.
Considering the fill factor, temperature rise caused a decline in FF for MAPbI 3 devices without the interface.In contrast, devices with the BiI 3 interface layer displayed a marginal increase in FF at higher temperatures.The rise can be explained by the possibility that the BiI 3 layer optimizes charge transport or minimizes series resistance under such conditions.On the other hand, MAGEI 3 -based devices exhibited stable FF values across temperature variations.However, incorporating the BiI 3 interface layer resulted in an enhanced FF as temperature surged.This increase could stem from the synergistic interplay between MAGEI 3 and BiI 3 , potentially enhancing charge extraction or reducing recombination at the interface.
Lastly, efficiency assessments of both MAPbI 3 and MAGEI 3 systems, regardless of the BiI 3 interface's presence, unveiled a decline with rising temperatures.This is a holistic outcome of the combined impact on J sc , V oc , and FF, and resonates with the commonly understood behavior that elevated temperatures often deteriorate the performance metrics of many photovoltaic materials.

Conclusion
In conclusion, our detailed study highlights the benefits of introducing a Bismuth Iodide (BiI 3 ) interlayer (IL) at the interface between the absorber and the HTL.Two different perovskites of MAPbI 3 and MAGeI 3 are used alongside Titanium Dioxide (TiO 2 ) as the ETL and Spiro-OMeTAD as HTL.Utilizing the SCAPS-1D simulation tool, we were able to clarify the mechanisms that contribute to the improved efficiency resulting from the BiI 3 integration.Notably, simply adding a BiI 3 layer at the perovskite-HTL interface significantly improves hole extraction by effectively reducing defect states, which in turn lowers charge recombination and ion migration.This strategic addition results in better device performance compared to traditional setups.The PCE of both MAPbI 3 and MAGeI 3 PSCs saw a considerable increase, showcasing the potential of BiI 3 IL for practical PSC applications.The efficiency witnessed a rise from 19.28 to 20.30% for MAPbI 3 and from 11.90 to 15.57% for MAGeI 3 .Additionally, MAGeI 3 based PSCs saw an improved fill-factor from 50.36 to 62.85%, and a better J sc from 13.22 to 14.2 mA/cm 2 , signifying reduced recombination and improved charge extraction.The FF for MAPbI 3 based PSCs saw a minor decline, while the V oc slightly ascended from 1.24 to 1.25 V and J sc from 20.01 to 21.6 mA/cm 2 .Additionally, a thorough analysis of temperature variations revealed interesting findings.It was observed that while the performance of MAPbI 3 -based devices remained relatively stable with temperature changes, regardless of the BiI 3 interface layer, the efficiency of both MAPbI 3 and MAGeI 3 compositions decreased with rising temperatures.These temperature dependencies highlight the crucial role of the BiI 3 interface layer in not only adjusting charge dynamics but also in reducing the negative impacts of thermal stress on overall device performance.Detailed evaluations of layer thickness and doping gradients using SCAPS-1D reinforce the idea that the presence of BiI 3 IL is crucial for both performance and durability across perovskite structures.Although the inclusion of BiI 3 slightly increased the optimized thickness of MAPbI 3 , it was much more significant for MAGeI 3 .The optimized thickness increased from 0.4 to between 0.8 and 1 μm.While for doping, the V oc sees significant increase in structures having the BiI 3 as IL, especially from E15 to E17 cm −3 , emphasizing the interface's role in balancing charge extraction and recombination losses.By reducing defect states and limiting recombination pathways, and providing resistance against temperature variations, the BiI 3 layer could play a significant role in addressing stability issues while also enhancing PSC performance metrics.Overall, our results suggest that the strategic addition of a BiI 3 interfacial layer within MAGeI 3 and MAPbI 3 -focused PSCs marks a significant advancement in sustainable energy conversion technologies, especially in settings with notable temperature variations.
Figure 1.(a) Nip structure of PSC without IL, (b) PSC with interface layer.

Figure 3 .
Figure 3. MAPbI 3 and MAGe 3 band alignment with and without a BiI 3 layer.

Figure 4 .
Figure 4.The current-voltage (I-V) characteristic curves of photovoltaic devices both with and without a BiI 3 interface layer.

Figure 5 .
Figure 5. Impact on J sc , V oc , FF and PCE while changing absorber thickness in presence and absence of BiI 3 IL.

Figure 6 .
Figure 6.Impact on J sc , V oc , FF and PCE while changing absorber doping in presence and absence of BiI 3 IL.

Figure 7 .
Figure 7. Effect of temperature variation on MAPbI 3 and MAGeI 3 on with and without BiI 3 interface layer.
48Kim et al. employed conformal quantum dot-SnO 2 layers as electron transporters, achieving a PCE of 25.7%.This approach not only improved charge extraction but also underscored the potential of integrating quantum dots with traditional ETLs to push the limits of PSC efficiency45.Li et al. enhanced PSC performance through the modification of interfaces using a multifunctional fullerene derivative for TiO 2 surface passivation.This method notably improved charge extraction, leading to a 20.7% improvement in PCE and highlighting the importance of surface passivation in achieving high-efficiency PSCs46.Salado et al. utilized thiazolium iodide for interface engineering, reducing thermal diffusion and significantly improving PCE.This strategy demonstrates the effectiveness of surface functionalization in enhancing both the efficiency and stability of PSCs, providing a promising route for future advancements47.Li et al. used interface ion exchange techniques to passivate surface defects, resulting in an extremely high open-circuit voltage of 1.19 V and an efficiency of 20.32%.This approach not only addresses surface defects but also opens new avenues for improving the photovoltaic performance of PSCs through ion exchange mechanisms48.Jiang et al. highlighted the excellence of SnO 2 as an ETL, owing to its superior band alignment and high electron mobility.This technique is crucial for enhancing charge extraction, a key factor in the efficiency of PSCs, and points towards the potential of SnO in paving the way for the next generation of solar cells

Table 1 .
Summary of discussed studies.

Table 2 .
Modeling parameter of the layers used in PSC.

Table 3 .
VBO and CBO on interfaces.

Table 4 .
Comparative impact of passivation layers on the PCE of perovskite solar cells.