A dielectric SiO₂ nanosphere array-assisted optical confinement strategy for high-efficiency and lead-reduced MAPbI₃ perovskite solar cells

Abstract

Perovskite solar cells (PSCs) are currently limited by a critical trade-off between the need for thick absorber layers (1000–1500 nm) to ensure sufficient light absorption and the environmental concerns regarding high lead (Pb) toxicity. While metal-based general light-trapping strategies like plasmonics or surface texturing have been explored, they often involve complex fabrication or offer marginal gains with high reflective loss. In this work, we present a high-performance, lead-reduced strategy using an optimized array of SiO₂ dielectric material-based nanospheres which can confine and scatter light with almost zero loss. By embedding a 61 nm diameter three-sphere array 50% into the FTO layer, we achieve significant optical confinement via angular scattering. This mechanism allows a thin 300 nm MAPbI₃ layer to achieve a 10.7% enhancement in average absorption, raising the short-circuit current density (J_sc) to 29.11 mA cm⁻² and the power conversion efficiency (PCE) from 22.58% to 24.61%. Crucially, this architecture enables a 73.78% reduction in lead content without sacrificing performance. This approach provides a scalable and eco-friendly pathway for the development of stable, high-efficiency, and low-toxicity next-generation photovoltaics.

(a) Proposed PSC with SiO₂ nanospheres embedded in the FTO layer, followed by ETL, MAPbI₃ absorber, HTL, and Au. (b) Optical mechanism of the nanospheres. (g) Absorption, transmission, and reflection spectra with and without SiO₂ nanospheres.

1. Introduction

The increasing global energy demand, expected to grow by 25–30% by 2040, along with environmental concerns linked to fossil fuels, has prompted a global transition toward renewable energy.^1–4 Fossil fuels currently supply about 77% of primary energy but account for approximately 89% of CO₂ emissions from the energy sector, accelerating climate change and environmental degradation.^1,2 These resources are also finite—oil reserves, for example, may be exhausted in the next 50 years under current consumption rates.^2,3 In contrast, renewable sources like solar, wind, biomass, hydropower, and ocean energy offer cleaner, sustainable alternatives. A fully renewable scenario could meet over 90% of global electricity demand while drastically cutting emissions.^3,4 Solar energy stands out due to its abundance and geographic versatility—173 000 terawatts of solar power continuously reach Earth, over 10 000 times the global energy use.^7–10 Unlike wind or hydro, solar power can be harnessed in diverse environments, including cities and deserts, with simple infrastructure.^5–8 Additionally, it offers low operating costs and minimal environmental impact during use, making it central to long-term sustainability.^11,12

Photovoltaic (PV) technologies are broadly classified into generations. First-generation crystalline silicon (mono- and polycrystalline) cells have achieved 20–22% efficiency but remain expensive and rigid.^13–15 Second-generation thin-film technologies (a-Si, CdTe, CIGS) reduce cost and material use but generally suffer from lower efficiency and toxic components.^13–15 Third-generation PV aims to overcome these drawbacks using novel materials and architectures—most notably, perovskite solar cells (PSCs), which have rapidly surpassed 25% efficiency within a decade. PSCs combine low-cost solution processing (estimated at $0.10–0.20 per W), tunable bandgaps (1.2–1.6 eV), high absorption, and mechanical flexibility, and are compatible with tandem designs.^{5–8,15–17} However, their commercialisation is challenged by intrinsic instability under heat, moisture, and UV exposure, and toxicity concerns over lead content. While tin (Sn) and germanium (Ge) have been explored as lead-free alternatives, they often face performance and stability issues.^18–22 More recently, fourth-generation PV has emerged, combining organic and inorganic nanostructures—such as tandem junctions, hybrid cells, and plasmonic or photonic structures—to enhance light harvesting and charge transport.²³

This work focuses on PSCs due to their compelling efficiency, affordability, and material versatility. Their low-temperature processability, suitability for flexible substrates, and strong research momentum position them as prime candidates for next-generation solar technologies.^18–20 Their tunable optoelectronic characteristics also allow flexible optimization,²³ aligning with the overarching goal of sustainable and scalable solar solutions.

For instance, in 2020, A. Mohsen et al.²² reported a 12.9% PCE for MASnI₃-based PSCs, which improved to 20% after incorporating ZrN/SiO₂ core–shell nanoparticles. Despite this advance, commercial viability remains limited by Sn²⁺ oxidation, which causes self-doping and rapid device degradation. The main problem is they use MASnI₃ as an absorber which band gap is 1.3 eV, so the absorption edge is 954 nm wavelength, in their results, they shown that they got almost 80%+ absorption from 950 nm to 1300 nm wavelength, which is very much unrealistic.²⁴ Moreover, the cost of tin-based materials ($50–100 per kg) adds further economic burden.¹⁵

A more recent study by Jan S. T. et al.²³ explored MAGeI₃-based PSCs using nine transport layer combinations, achieving a peak PCE of 25.43%. Despite these promising results, Ge-based PSCs face challenges such as a wide 1.6 eV bandgap, defect sensitivity, and high material cost—Ge currently costs about $1500 per kg—hindering large-scale deployment.¹⁵ Additional concerns include scaling issues, toxicity in some transport layers, and limited long-term performance data.^24,25

Overall, lead-free PSCs still underperform compared to their lead-based counterparts in both efficiency and long-term stability. Tin-based PSCs suffer from Sn²⁺ oxidation, resulting in increased dark current and performance loss, while germanium-based cells are limited by their wide bandgap and high defect sensitivity. Furthermore, many alternative transport materials introduce toxicity, poor carrier mobility, and low open-circuit voltages—further complicating commercial adoption.²⁴

To improve the efficiency of thin absorber layers in PSCs, light-trapping strategies have been widely explored.^25,26 These include nanostructured layers, metallic nanoparticles (e.g., Ag, Al), microlens arrays, and prism structures to increase the optical path length and absorption.^27–31 While promising, these approaches introduce challenges. Nanoparticle embedding can create surface defects, increasing non-radiative recombination and reducing carrier lifetime.^32,33 Metallic nanoparticles may cause local heating, affecting thermal stability and accelerating degradation.^34,35 Prism and microlens arrays complicate fabrication, raise costs, and may suffer from performance variability under changing light angles,^20,21 making them harder to scale.

Despite these limitations, some advances stand out. Wang et al.³⁵ achieved a 21.16% PCE using prism structures, while Shorok Elewa et al.³³ reached 26.06% using a simpler method, placing a single SiO₂ nanosphere atop the FTO layer in a MAPbI₃-based PSC, because dielectric material confine and scatter light without absorbing and creating heat unlike metal nanosphere. This avoided embedding-related defects but offered limited absorption enhancement at longer wavelengths compared to plasmonic methods. But the same simulation setup problem is also present here: Shorok Elewa et al. use MAPbI₃ with a bad gap of 1.55 eV as an absorber, so the absorption edge is 800 nm, but they show high absorption from 800 nm to 100 nm, which is totally unrealistic. To further enhance light capture, M. Mashrafi et al.³⁶ embedded a gold nanoparticle array inside the perovskite layer, simulating a PCE of 30.4%, a J_sc of 39.42 mA cm⁻², and an FF of 70.05%. However, their optical simulations ignored radiative recombination, likely overestimating efficiency. Moreover, their SCAPS-1D-based electrical modelling couldn't simulate embedded nanoparticles, creating a disconnect between optical and electrical predictions. They also failed to consider the reduced absorber volume due to nanoparticle inclusion, a key point raised by A. M. Acevedo.³⁷ Beyond these modelling issues, nanoparticle embedding disrupts the crystal structure, raising defect density and recombination rates and increasing series resistance and localised heating—factors detrimental to device longevity. Furthermore, the high cost and complexity of gold nanoparticle arrays present additional barriers to commercial viability. This model also shows unrealistic very high absorption from 800 nm to 1200 nm wavelengths, where the absorption edge is 800 nm.

In the present study, a novel, highly efficient, and fabrication-friendly light-trapping architecture is introduced to address the limitations of earlier approaches. This design overcomes issues associated with embedding plasmonic materials within the absorber, the complexity of fabricating intricate light-trapping structures (such as prism-shaped, star-shaped, or graded microstructures), and the reduced PCE typically observed in thin absorber layers. The proposed structure incorporates three SiO₂ nanospheres, each with a diameter of 61 nm and a 2 nm interparticle spacing, partially (50%) embedded into the fluorine-doped tin oxide (FTO) layer. This simple, symmetric configuration enhances optical scattering and induces localized resonances, significantly improving light absorption in the 300–827 nm range, unlike single nanospheres which show higher absorption at higher wavelength beyond bandgap.

Optical simulations reveal the total integrated absorption improves by 10.7% from 0.71558 (without SiO₂) to 0.79218 (with SiO₂). Electrical simulations further validate this enhancement, with the short-circuit current density (J_sc) increasing from 26.80 mA cm⁻² to 29.11 mA cm⁻² (8.61% enhanced the current density; it is lower than light absorption because the electrical simulation coincides with radiative and nonradiative recombination) and the power conversion efficiency (PCE) rising from 22.58% to 24.61%, representing a 9% improvement. The slight discrepancy between optical (10.7%) and electrical (9%) enhancements occurs due to losses explicitly considered in electrical simulations, such as radiative and non-radiative recombination, series resistance, and thermal dissipation. Notably, this is the first report to demonstrate such a significant efficiency gain using only three dielectric nanospheres, made possible through precise control of their size, spacing, and position.

This method offers a low-cost, scalable, and highly practical solution for improving perovskite solar cell performance. The reported PCE from a planar MAPbI₃ absorber is 24.5%, achieved using a thick 1110 nm absorber layer, as demonstrated by A. A. B. Baloch et al.³⁸ In contrast, a PCE of 24.61% is achieved here with only a 300 nm-thick MAPbI₃ absorber, representing a 73.78% reduction in absorber thickness. This significant reduction lowers toxic Pb content, which is vital for environmental safety. While the thickness reduction may seem modest at the single-cell level, it becomes substantial when scaled to mass production of Pb-based solar cells. In addition to reducing Pb toxicity, the thinner absorber decreases material costs, especially since SiO₂ nanospheres used for light management are far less expensive than MAPbI₃ perovskite.

Moreover, since SiO₂ is chemically stable, non-toxic, and environmentally benign and widely used in pharmaceuticals, food products, and cosmetics, it makes an eco-friendly addition to solar cell structures. Their chemical stability arises from the strong Si–O bond (bond energy is 800 kJ mol⁻¹), which resists degradation under heat, moisture, UV exposure, and acidic or basic environments. This intrinsic robustness ensures long-term stability in real-world photovoltaic conditions.³⁹ Although adding SiO₂ nanospheres to the device structure involves extra fabrication steps, these steps are usually done using simple, low-energy chemical methods like the sol–gel or Stöber process. These techniques work at relatively low temperatures and use safe, commonly available chemicals such as TEOS and ethanol. Compared to traditional high-temperature or vacuum-based coating methods, this makes the overall process much less demanding in terms of energy and environmental impact. So, even though the process becomes slightly more complex, its effect on the environment is still very small. Because SiO₂ is abundant, chemically stable, and compatible with easy and scalable fabrication methods, its use supports the goal of building solar cells that are both efficient and environmentally friendly.

While a complete life cycle assessment (LCA) of this process is not included in this study, we acknowledge its importance and recommend it as a valuable direction for future work to fully understand the long-term environmental effects of using such nanostructures in solar cells.^40–43 Radiative recombination is included in all simulations to ensure accurate and realistic results. This approach provides an efficient and cost-effective way to reduce material usage and environmental impact, making large-scale production of perovskite solar cells more practical. It also shows strong potential for use in other thin-film solar technologies, like silicon, III–V, and II–VI semiconductors, where effective light trapping continues to be a significant challenge.

2. Model design and material selection

2.1. Structure and materials selection

The perovskite solar cell (PSC) structure used in this study was carefully designed with multiple functional layers to optimise both light absorption and charge transport, as shown in Fig. 1. As the back contact, we use 50 nm thick Au. Gold was chosen for its excellent electrical conductivity and chemical stability, which help ensure efficient charge collection and reduce energy loss at the electrode interface. However, alternative metals like Ag, Cu, Al or carbon, though they have higher potential, often suffer from high oxidation problems (Ag, Cu), lower work function alignment (Al) or reduced conductivity (carbon), potentially affecting device performance and stability.³³ At the bottom, a 50 nm gold (Au) layer serves as the back contact. Above the gold layer is a 200 nm layer of Spiro-OMeTAD, which functions as the hole transport layer (HTL). Spiro-OMeTAD is well known for its high hole mobility, strong energy-level alignment with perovskite materials, and good film-forming properties. These characteristics support effective hole extraction and reduce the chances of recombination.^32,33

Fig. 1. Proposed PSC structure with SiO₂ nanospheres. The SiO₂ nanoparticle was embedded within the FTO layer, followed by ETL, MAPbI₃, HTL and gold substrate.

The light-absorbing perovskite layer, 300 nm thick, is placed above the HTL. This thickness was selected to achieve a balance between strong optical absorption and efficient carrier transport. Thicker layers are good for light absorption because they enhance light absorption, but at the same time they increase the recombination rate. The optimal thickness of MAPbI₃ absorber is around 1000 nm without any light enhancement mechanism 1000 nm thicker absorber can provide around 24% PCE, but the target of this work is to achieve more than 24% PCE using a thinner absorber. A 300 nm thick absorber is the optimal absorber to achieve this goal. The material used is CH₃NH₃PbI₃ (MAPbI₃), which has a direct bandgap of around 1.50 eV, a high absorption coefficient, long carrier diffusion lengths, and excellent defect tolerance. These properties make it suitable for efficient light harvesting and charge movement in thin-film devices. Finally, a 50 nm layer of titanium dioxide (TiO₂) is used as the electron transport layer (ETL). TiO₂ offers high electron mobility, strong electron selectivity, and good band alignment with MAPbI₃, which helps reduce recombination at the interface and ensures fast and efficient electron extraction.

A 100 nm thick fluorine-doped tin oxide (FTO) layer acts as the transparent conductive electrode, offering a good combination of high electrical conductivity and excellent optical transparency in the visible spectrum, which ensures efficient photon entry while maintaining low series resistance. To improve light harvesting, this work introduces SiO₂ nanospheres. The optimised diameter of the nanosphere is 61 nm, and optimised pitch of the nanosphere is 63 nm (surface-to-surface distance is 2 nm). And the optimised position of the nanosphere is 50% inside of the FTO. This positioning enabling strong light scattering and increases the optical path length, especially at longer wavelengths. SiO₂ was chosen for its excellent optical transparency, low absorption loss, chemical stability, and ease of fabrication, making it an ideal candidate for light-trapping applications.

2.2. Simulation setup

To get accurate results from the simulation, it is very important to set up the model properly. Simulation software sometimes exaggerates results. In optical simulation, it is very important to set up RI properly aligned with the bandgap. In practical cases, the imaginary part of RI is not zero after the band gap edge, so if we can confine light inside the absorber, simulation tools may show higher absorption after the absorption edge, but in reality, it will not happen because electrons in the valence band will not have enough energy to jump from the valence band to the conduction band. To solve this problem, there are two available solutions. Firstly, use an identical mesh for both sides of the periodic condition. Secondly make the value of the imaginary part of RI zero after the band gap. For example, in the case of MAPbI₃ with a band gap of 1.50 eV, the absorption edge is 827 nm, so if we simply set the value of Im(RI) to zero after all wavelengths exceeding 827 nm. Another concern is that sometimes individuals take the RI value up to the bandgap edge; this can also create problems because simulation tools often use the last given value for all other values that are not specified.

In this study, COMSOL Multiphysics was employed due to its robust capabilities in handling coupled optical and electrical simulations. To address the meshing challenges associated with sub-wavelength nanostructures, we used COMSOL's built-in adaptive mesh refinement feature. An initial adaptive mesh study was performed to generate a refined mesh distribution that accurately resolves the nanoscale features, particularly around the embedded SiO₂ spheres. This mesh was then used consistently across the simulations to ensure accuracy. The mesh consists of 17 422 tetrahedral elements and 3426 triangular surface elements, with a total of 3454 mesh vertices. The average element quality was 0.6583, indicating a well-structured and reasonably high-quality mesh suitable for accurate simulations. The minimum element quality was 0.233, which is within acceptable limits for reliable results. The total mesh volume was calculated to be 2.749 × 10⁷ nm³, confirming a symmetric distribution centred around higher-quality elements and supporting the reliability of the simulation outcomes.

In real device structures, a protective glass layer is typically used as the top cover to shield the solar cell from environmental exposure while maintaining high optical transmission. However, for the purposes of this optical simulation, a 500 nm air layer was applied above the device to simplify boundary conditions and focus on light interaction with the SiO₂ nanospheres and active layers. This approach allows accurate prediction of absorption enhancement trends while isolating the effect of the light management structure.

To overcome limitations commonly associated with numerical simulations reported by A. M. Acevedo,³⁷ such as idealized layer assumptions, constant optical parameters, and lack of interface-level phenomena, this study employs COMSOL Multiphysics' wave optics module and semiconductor module in an integrated manner. The optical model is constructed using realistic 3D geometry and experimentally derived wavelength-dependent refractive index data. It captures complex interactions such as near-field scattering, plasmonic effects, and interference from partially embedded SiO₂ nanospheres. Periodic boundary conditions and perfectly matched layers (PML) are applied to minimize artificial reflections, enabling precise evaluation of light-trapping effects and spectral absorption across the active region of the perovskite solar cell (PSC).

On the electrical side, the spatially resolved optical power dissipation (ewfd.Q_rh, representing the resistive heating power density from the electromagnetic waves, frequency domain interface) obtained from the optical simulation is mapped as the volumetric generation rate within the drift-diffusion framework. This approach ensures that charge carrier generation reflects actual absorption profiles, rather than relying on uniform or idealized distributions. The model also incorporates radiative and nonradiative recombination, field-dependent transport, and realistic material parameters to more accurately simulate device performance. While full quantum-level coupling of nanoparticles to semiconductor physics remains beyond standard COMSOL capabilities, this method provides a computationally efficient yet physically meaningful route to analyze light–matter interaction and carrier dynamics. Although environmental degradation under operational stress (e.g., UV, heat, and humidity) is not modelled, the present framework offers valuable steady-state insight into performance trends driven by nanophotonic enhancement.

To validate the optical-to-electrical consistency, the spatially resolved optical power dissipation (Q_rh) was calculated using the wave optics module and directly coupled as a volumetric generation rate into the semiconductor module. This ensures that the light confinement effects are physically mapped to the carrier generation profile.

2.3. Light trapping process

Fig. 2(a) represents the optical behaviour of the perovskite solar cell structure without any nanospheres on top of the FTO layer. In this setup, when light enters the device, a significant portion is either reflected at the air/FTO interface or passes through the structure with limited interaction inside the absorber layer.⁴⁴ Since the incident light follows mostly direct paths, the optical path length within the active layer remains short, which reduces the probability of photon absorption. As a result, much of the incident light energy is lost either through reflection or transmission, limiting the generation of charge carriers and directly affecting the overall efficiency of the solar cell.⁴⁵

Fig. 2. Shows the light-trapping mechanism of (a) without a nanosphere and (b) with a nanosphere. Whereas the SiO₂ nanoparticle array was embedded within the FTO layer.

In contrast, Fig. 2(b) illustrates the optical mechanism when three SiO₂ nanospheres are placed on the FTO surface, with each sphere positioned so that approximately 50% of its volume is embedded in the FTO and 50% is exposed to air. This arrangement plays a crucial role in enhancing light absorption by inducing strong light scattering at the air–SiO₂–FTO interfaces.^44,45 When light encounters the nanospheres, it is scattered into a variety of angles rather than passing straight through, which effectively increases the optical path length inside the perovskite absorber layer.⁴⁴ The longer light remains inside the active layer, the higher the probability of absorption, which leads to enhanced photocurrent generation.⁴⁵ Additionally, the refractive index contrast between air, SiO₂, and FTO further supports efficient light trapping, making this nanosphere-based strategy an effective way to boost the solar cell's optical performance without increasing the absorber layer thickness.^44–46

Although there are several alternative methods of light trapping, for example, prism-based, metallic nanoparticle array, square-based, or surface engineering, these methods are effective and can provide better results, but they have their own problems.^27–31 For prism-based structures, results are usually good, but managing the prism angle is very crucial during practical fabrication, which restricts their mass production.^20,21 Again, metallic nanoparticles are good; they work by LSPR and show very good absorption, but they often increase surface defects inside the absorber and increase the recombination rate.^34,35 On the other hand, spherical shapes are very easy to fabricate; there is no scaling problem. So, it is very easy to achieve mass production from this kind of structure.

The light confinement mechanism is primarily driven by the refractive index contrast between the air, the SiO₂ nanospheres, and the FTO layer. When incident light interacts with the partially embedded three-sphere array, the nanospheres act as scattering centers that redirect the incoming wavefront into higher-order angles. This angular scattering increases the effective optical path length of photons within the 300 nm MAPbI₃ layer, allowing for significant light trapping without increasing the physical thickness of the absorber. Furthermore, the 2 nm interparticle spacing facilitates near-field coupling, which concentrates the electromagnetic field at the perovskite/ETL interface. This is validated by the 10.7% enhancement in integrated absorption, confirming that the nanostructures successfully trap light that would otherwise be reflected or lost in a standard planar configuration.

2.4. Fabrication process of the model

As shown in Fig. 3, the fabrication process of the proposed PSC starts with a glass substrate coated with FTO, which acts as the transparent conductive electrode.^16,17 To ensure proper adhesion of the layers and maintain cleanliness, the substrate undergoes a thorough multi-step cleaning process using ultrasonication.⁴⁷ First, it is placed in acetone and sonicated for 15 minutes to remove any organic contaminants. This is followed by another 15-minute sonication in isopropyl alcohol (IPA) to get rid of residual grease. Finally, the substrate is rinsed with deionized (DI) water to remove any remaining particles or solvents. After cleaning, the substrate is dried either by blowing nitrogen gas over it or by placing it on a hot plate at 100 °C for a few minutes.⁴⁸

Fig. 3. Schematic illustration of the fabrication workflow for the perovskite solar cell (PSC) featuring embedded SiO₂ nanospheres for enhanced light management, progressing from the initial planar FTO substrate to the finalized complete device architecture.

Next, the fabrication of the proposed device begins with the synthesis of monodisperse SiO₂ nanospheres (61 nm diameter) using a low-temperature sol–gel Stöber process involving tetraethyl orthosilicate (TEOS) and ethanol. The FTO-coated glass substrate is prepared via a sequential 15-minute ultrasonication cleaning in acetone, isopropyl alcohol, and DI water, followed by drying at 100 °C. To ensure the precise 50% embedding of the nanospheres, the FTO surface is pre-patterned using Reactive Ion Etching (RIE) to create shallow wells of controlled depth. The nanospheres, dispersed in ethanol, are then deposited into these sites via the Langmuir–Blodgett technique or controlled spin-coating to form a highly ordered array with a 2 nm interparticle spacing, followed by a mild annealing step at 80 °C to ensure firm adhesion. This controlled positioning is critical for reproducing the localized resonances and light scattering effects required for the reported 10.7% absorption enhancement.^40,41

After the nanospheres are deposited, the substrate is gently heated to around 70 to 80 °C to help the nanospheres stick firmly and to evaporate any remaining solvent.^43–45 This mild annealing step also improves particle–substrate adhesion and reduces surface defects—a process confirmed by studies on aerosol–gel- and sol–gel-derived SiO₂ thin films. For instance, annealing SiO₂ films at 100–150 °C significantly improved film density and adhesion to substrates in thin-film solar and optical coatings.⁴³

Following this, a 50 nm thick ETL of TiO₂ is applied using a sol–gel method.⁵⁰ A precursor solution made of titanium isopropoxide, ethanol, and hydrochloric acid is spin-coated onto the surface. The substrate is then annealed at 450 °C for 30 minutes to form a compact and crystalline TiO₂ layer, which helps extract electrons efficiently and reduces charge recombination at the interface.^51,52 Once cooled, a 300 nm thick perovskite absorber layer, usually methylammonium lead iodide (CH₃NH₃PbI₃) is deposited using a one-step spin-coating method.³² In this process, a precursor solution containing PbI₂ and CH₃NH₃I dissolved in a DMF/DMSO solvent mixture is spin-coated in two stages. During the final seconds of spinning, an anti-solvent such as chlorobenzene is dropped onto the rotating substrate to promote rapid crystallization. The film is then annealed at 100 °C for 10 to 15 minutes to form a uniform, high-quality perovskite layer.^32,49

After forming the absorber layer, a 200 nm thick hole transport layer (HTL) of Spiro-OMeTAD is applied by spin-coating.⁴⁹ The Spiro-OMeTAD solution is prepared in chlorobenzene with additives like lithium bis(trifluoromethanesulfonyl)imide (Li-TFSI) and 4-tert-butylpyridine to improve hole mobility. The coated substrate is then left in ambient air for several hours to allow controlled oxidation of Spiro-OMeTAD, which is essential for achieving high conductivity.³⁹ To complete the device, a 50 nm thick gold (Au) back electrode is deposited using thermal evaporation or sputtering under high vacuum. A metal shadow mask is used during this step to define the active area of the cell, typically around 0.1 to 0.2 cm².⁵²

Although the simulation model includes a 500 nm air layer above the device to mimic real-world optical effects, actual devices often replace or cover this layer with glass or polymer encapsulation to protect the solar cell from moisture, oxygen, and other environmental damage. This multilayer fabrication strategy, including the innovative use of partially embedded SiO₂ nanospheres, leads to better light absorption, reduced optical losses, and improved power conversion efficiency. It also offers enhanced device stability and provides a pathway for scalable, high-performance perovskite solar cells.^16,17

To translate the theoretical findings of this work into practical applications, several experimental challenges must be addressed. First, the uniformity of the SiO₂ nanosphere array is critical; techniques such as Langmuir–Blodgett assembly or controlled spin-coating are required to ensure a periodic monolayer over large-area substrates. Non-uniformity could lead to localized optical shunting or inconsistent absorption. Second, the interface between the perovskite and the nanostructures must be carefully managed. High-quality film deposition (e.g., via vacuum evaporation or modified two-step methods) is necessary to avoid the formation of structural voids or pinholes around the spheres, which would increase series resistance and facilitate charge recombination. Despite these fabrication complexities, the use of earth-abundant silica and the significant reduction in absorber volume provide a compelling argument for the development of nanostructured PSCs to achieve a superior balance between cost and performance.⁶⁴

The proposed model is compatible with existing fabrication techniques and large-scale manufacturing processes. As demonstrated in,⁶⁵ similar planar perovskite solar cell structures have already been experimentally fabricated using scalable deposition methods. In the proposed work, SiO₂ nanospheres are introduced to further enhance device performance. The SiO₂ nanospheres can be synthesized in large quantities using well-established chemical methods, and using RIE process, the nanospheres can be embedded inside the FTO easily, while the other device materials, including MAPbI₃, FTO, TiO₂, Spiro-OMeTAD, and the Au back contact, are already widely used in photovoltaic fabrication and can be deposited using scalable techniques. Therefore, compared to other closely related light-trapping models, the proposed structure offers a comparatively simpler, industry-compatible, and fabrication-friendly approach for large-scale production.⁶⁶

2.5. Material selection for simulation

In this study, the modelling of perovskite solar cells (PSCs) was conducted using COMSOL Multiphysics by integrating optical and electrical simulations through the wave optics and semiconductor modules.⁶⁷ The simulation workflow follows a two-step approach: first, optical modeling is performed to compute the photogeneration profile within the device; second, this data is used in the electrical model to simulate charge transport and recombination processes across the various layers. For the electrical simulation, material parameters such as carrier mobility, doping concentration, and recombination coefficients were sourced from Table 1. In contrast, the optical simulation employed COMSOL's built-in material properties to account for wavelength-dependent refractive indices and absorption coefficients, ensuring accurate modeling of light propagation and absorption within the PSC structure. The optical behavior of the PSC structure was analyzed by solving the Helmholtz equation in the frequency domain:¹⁰

∇(∇ × E) − k₀²n²(r)E = 0 1

where E is the electric field vector, k₀ = 2π/λ is the free-space wave number, and n(r) is the complex refractive index distribution across the multilayered geometry.³³ Each material in the device—FTO, TiO₂, perovskite (CH₃NH₃PbI₃), Spiro-OMeTAD, and gold—was assigned its own wavelength-dependent complex refractive index (n + ik) for accurate optical simulations.^9–12 From the spatial electric field distribution, the local absorption was used to calculate the optical generation rate as:¹²

2

where α(λ) is the absorption coefficient, I(λ) is the incident light intensity, hν is the photon energy, and z is the depth into the material.^12–15 This spatial generation rate forms the basis for evaluating how much photogenerated charge is available for collection in the electrical model.

Table 1. Key parameters of the layers in the simulated perovskite solar cell structure.

Parameters	Spiro-MeOTD	CH3NH3PbI3	TiO2	FTO
Thickness (nm)	200	300	50	100
Relative permittivity, εr	3 (ref. 53)	6.5 (ref. 57)	9 (ref. 57)	9 (ref. 59)
Band gap, Eg (eV)	3 (ref. 53)	1.50 (ref. 57)	3.2 (ref. 57)	3.5 (ref. 59)
Electron affinity, χ (eV)	2.45 (ref. 53)	3.6 (ref. 58)	4 (ref. 57)	4 (ref. 59)
Effective density of states, valence band, Nv (cm−3)	1020 (ref. 53)	5 × 1018 (ref. 54)	1019 (ref. 59)	1.8 × 1019 (ref. 59)
Effective density of states, conduction band, Nc (cm−3)	1020 (ref. 53)	5 × 1018 (ref. 54)	1019 (ref. 59)	2.2 × 1018 (ref. 59)
Electron/hole mobility, µe/µp (cm2 V−1 s−1)	2/0.01 (ref. 54)	50/50 (ref. 57)	0.01/2 (ref. 54)	20/10 (ref. 57)
Acceptor concentration, NA (cm−3)	2 × 1016 (ref. 55)	3 × 1015 (ref. 55)	—	—
N D (cm−3)	—	—	2 × 1018 (ref. 54)	2 × 1019 (ref. 55)
Electron/hole lifetime, SRH, τe/τp (ns)	5/5 (ref. 56)	100/100 (ref. 54)	5/5 (ref. 56)	—

Once the photogeneration profile is obtained, it is fed into the semiconductor module to simulate carrier transport using the coupled Poisson and drift-diffusion equations. The electrostatic potential φ is obtained from Poisson's equation:¹⁰

∇ × (ε∇ϕ) = −q(p − n + N^D+ − N^A−) 3

where ε is the dielectric permittivity, q is the elementary charge, p and n are the hole and electron concentrations, and N^D+ and N^A− are ionized donor and acceptor densities.^10,11 Charge transport for electrons and holes is governed by the continuity equations:¹²

4

5

where D_n and D_p are the diffusion coefficients, µ_n and µ_p are the mobilities of electrons and holes, respectively, G is the generation rate (from the optical module), and R is the net recombination rate.^10–14 Recombination is accounted for using three primary mechanisms: Shockley–Read–Hall (SRH), radiative, and Auger recombination. The SRH recombination is modelled as:³³

6

where τ_n and τ_p are the lifetimes for electrons and holes, and n_i is the intrinsic carrier concentration.³³ Radiative recombination is expressed as

R_rad = B(np − n_i²) 7

where B is the radiative recombination coefficient.^13,14 Auger recombination, although minimal in perovskites, is also included and is defined as:³³

R_Auger = C_nn(np − n_i²) + C_pp(np − n_i²) 8

where C_n and C_p are the Auger coefficients for electrons and holes.^32,33

In terms of device architecture, appropriate boundary conditions are defined to represent real-world operation. The FTO front contact is treated as an ohmic electron-selective contact, and the gold (Au) back contact serves as an ohmic hole-collecting electrode. Interface conditions are also implemented to ensure continuity of electric potential and current density across material boundaries.³³ The optical enhancement in this study involves the introduction of SiO₂ nanospheres at the front surface, with 50% of each nanosphere embedded in the FTO layer and the remaining 50% extending into air. These nanospheres improve light scattering and increase the optical path length, which enhances absorption in the 300 nm perovskite absorber without increasing its thickness. A 500 nm air layer is also added to replicate realistic front-side optical behaviour.⁴⁴

Simulations are conducted under standard AM1.5G solar illumination (1000 W m⁻²), and a voltage sweep is applied to extract current–voltage (J–V) characteristics. The performance parameters evaluated include short-circuit current density (J_sc), open-circuit voltage (V_oc), fill factor (FF), and power conversion efficiency (PCE). The mesh is finely tuned, especially near interfaces and around the SiO₂ nanospheres, to capture accurate field and carrier dynamics.^60,61 By leveraging this multiphysics framework in COMSOL, the study successfully analyzes both optical and electrical performance of PSCs and evaluates the impact of light-trapping structures on device efficiency, stability, and commercial viability.

3. Results and discussions

3.1. Structural optimization of dielectric material

Fig. 4 presents the step-by-step optimization of SiO₂ spheres to enhance light absorption in the perovskite solar cell. In Fig. 4(a), the effect of SiO₂ sphere position is examined. When the spheres are positioned on the top of the FTO (0% inside FTO), the average absorption is 72.82%, but embedding them slightly (10% inside FTO) causes a slight increase in absorption (0.7286). As the spheres are more embedded, absorption rises significantly, reaching 72.92% at 25% inside FTO, and when positioned 40% inside FTO the average absorption rises to 73.21%; the peak absorption comes from 50% embedded in FTO that is 73.67%. Moreover, 50% embedding of SiO₂ shows the maximum absorption because it provides an optimal RI contrast at the air/SiO₂/FTO interface. This enhances forward scattering and constructive light coupling inside the absorber. Further embedding beyond this point leads to a slight reduction in absorption (72.78% at 60% inside FTO and 73.04% at 70% inside FTO).

Fig. 4. Optimization of SiO₂ spheres for enhanced light absorption (green markers indicate the optimal point in each case): (a) effect of sphere position, (b) effect of sphere number, (c) effect of pitch (surface-to-surface distance), (d) effect of sphere diameter.

Fig. 4(b) investigates the effect of varying the number of SiO₂ spheres placed in the optimised position from Fig. 4(a). Starting with one sphere, absorption is 73.67%, and it slightly decreases to 73.26% with two spheres because of destructive interference inside the absorber. The absorption reaches its highest value of 74.45% with 3 spheres, because instead of destructive interference in this condition, the absorber experiences constructive interference. However, as the number of spheres increases to 5 and 9, the absorption slightly decreases to 74.03% and 73.5%, respectively. This suggests that 3 spheres is the optimal number, and further increases lead to diminishing returns or potential optical losses due to scattering or interference effects.

Next, Fig. 4(c) shows the effect of the surface-to-surface distance (pitch) between SiO₂ spheres on the average light absorption. At a pitch of 1 nm, the absorption is 74.29%, and it increases to 77.92% at 2 nm, indicating a significant improvement in light trapping with a slight increase in spacing. However, as the pitch increases to 3 nm and 4 nm, the absorption decreases to 75.04% and 76.03%, respectively. This suggests that while a small pitch enhances light absorption, further increases in the spacing between spheres begin to reduce the effectiveness of light scattering and trapping. The optimal pitch for maximising absorption appears to be around 2 nm.

Finally, Fig. 4(d) illustrates the effect of SiO₂ sphere diameter on the average light absorption. With a 60 nm diameter, the absorption is 77.76%, and it increases to 79.21% at 61 nm, indicating a significant improvement in absorption with a slight increase in diameter. However, as the diameter increases further to 62 nm and 63 nm, the absorption decreases to 75.45% and 74.08%, respectively. This trend suggests that while increasing the diameter from 60 nm to 61 nm enhances light trapping, further increases beyond 61 nm lead to a reduction in absorption. Thus, an optimal sphere diameter around 61 nm is identified for maximizing light absorption.

In summary, the best configuration for maximizing light absorption in the perovskite solar cell involves placing 3 SiO₂ spheres, positioned 50% in air and 50% in FTO, with a 2 nm pitch and a 61 nm diameter for the spheres.

3.1.1. Fabrication tolerance analysis

To assess the manufacturability of the proposed design, a fabrication tolerance analysis was performed by evaluating the variation in optical absorption resulting from deviations of the optimized geometrical parameters. A performance deviation criterion of 1% relative to the optimized absorption was adopted to quantify the fabrication sensitivity of each parameter.

Fig. 5(a) shows the influence of the nanosphere embedding position within the FTO layer. The optimized structure corresponds to a 50% embedding depth with an average absorption of 0.7367. Reducing the embedding depth to 40% results in only a 0.62% change in absorption, whereas increasing it to 60% causes a 1.20% deviation. Therefore, the embedding position exhibits the highest fabrication tolerance among all investigated parameters, allowing approximately ±10 percentage points around the optimized value before the absorption changes by more than 1%.

Fig. 5. Fabrication sensitivity analysis of the optimized SiO₂ nanosphere array. The absorption response is evaluated by varying (a) the nanosphere embedding position inside the FTO layer, (b) the number of SiO₂ nanospheres, (c) the pitch between adjacent nanospheres, and (d) the nanosphere diameter around their optimized values. The optimized configuration corresponds to 50% embedding depth, three SiO₂ nanospheres, 2 nm pitch, and 61 nm diameter. The results demonstrate the robustness of the optimized structure against fabrication-induced variations and identify the parameters requiring tighter dimensional control during fabrication.

The effect of the number of SiO₂ nanospheres is presented in Fig. 5(b). The optimized configuration consists of three nanospheres with an average absorption of 0.7445. Increasing the number of nanospheres to five produces only a 0.55% reduction in absorption, while configurations containing two or six nanospheres lead to deviations exceeding 1%. This indicates that the optical response is relatively insensitive to moderate increases in nanosphere count but becomes more sensitive when the number of nanospheres deviates significantly from the optimum.

Fig. 5(c) illustrates the effect of pitch variation. The optimized pitch is 2 nm, yielding an average absorption of 77.93%. Deviations of only 1 nm from the optimized pitch produce absorption changes exceeding 2–4%, indicating that the optical response is highly sensitive to inter-particle spacing. Consequently, precise control of nanosphere placement is required during fabrication.

Similarly, Fig. 5(d) presents the effect of nanosphere diameter variation. The optimized diameter of 61 nm provides the highest absorption of 79.21%. A diameter reduction of 1 nm decreases the absorption by approximately 1.88%, while larger deviations produce even greater reductions. These results indicate that nanosphere diameter is one of the most critical fabrication parameters affecting device performance.

Overall, the tolerance analysis reveals that the embedding position and nanosphere number possess comparatively higher fabrication robustness, whereas the pitch and nanosphere diameter require tighter fabrication control. The observed behavior confirms that the proposed structure can maintain its enhanced optical performance under realistic fabrication variations while identifying the key dimensions that must be accurately controlled during device manufacturing.

3.2. Final results

In this study, optical simulations were first carried out using the RF module in COMSOL to calculate the solar absorption profile of the perovskite solar cell, both with and without the incorporation of SiO₂ spheres. The absorption data were then exported for further electrical analysis. Fig. 6 presents a detailed comparison of the electric field distribution and absorbed power at specific wavelengths, as well as the overall absorption profile for both cases. The absorption spectra shown in Fig. 6(m) clearly illustrate the improvement achieved by introducing SiO₂ spheres. Without SiO₂, the solar cell shows poor absorption, meaning much of the light passes through the absorber without contributing to power generation. However, once the SiO₂ spheres are incorporated, a significant increase in absorption is observed, confirming their role in enhancing light trapping and improving overall absorption. Fig. 6(a–l) support or validate the absorption spectrum shown in Fig. 6(m).

Fig. 6. Comparison of electric field distribution and absorbed power in the perovskite solar cell with and without SiO₂ spheres: (a–c) electric field distribution without SiO₂ at wavelengths of 330 nm, 550 nm and 825 nm, respectively; (d–f) absorbed power in the absorber layer without SiO₂ at 330 nm, 550 nm and 825 nm; (g–i) electric field distribution with SiO₂ at 330 nm, 550 nm and 825 nm; (j–l) absorbed power in the absorber layer with SiO₂ at 330 nm, 550 nm and 825 nm; (m) comparison of absorption, transmission, and reflection spectra of the solar cell with and without SiO₂ nanospheres.

Looking at the electric field distribution for the lower wavelength (330 nm) in Fig. 6(a) (without SiO₂) and Fig. 6(g) (with SiO₂), the distribution patterns appear quite similar. This observation is consistent with the absorption spectra in Fig. 6(m), which show little difference at shorter wavelengths regardless of the presence of SiO₂. The corresponding absorbed power profiles in Fig. 6(d) (without SiO₂) and Fig. 6(j) (with SiO₂) further confirm this, showing that at 350 nm, the absorption behaviour remains mostly unchanged.

At the intermediate wavelength of 550 nm, a notable difference is observed. Although 550 nm is a non-resonant point——meaning it does not correspond to a strong resonance peak—both the absorption and the electric field distribution are still significantly enhanced when SiO₂ spheres are introduced. As shown in Fig. 6(b) (without SiO₂) and Fig. 6(h) (with SiO₂), the electric field becomes more confined within the absorber layer due to the presence of SiO₂ spheres. The absorbed power profiles in Fig. 6(e) (without SiO₂) and Fig. 6(k) (with SiO₂) reflect this improvement, where even though the absorption at 550 nm is lower than at the resonant wavelength, it remains substantially higher compared to the case without SiO₂. This highlights that SiO₂ spheres can enhance absorption not only at resonant points but also at non-resonant wavelengths.

At the longer wavelength of 825 nm, corresponding to a resonant point, the effects are even more pronounced. As seen in Fig. 6(c) (without SiO₂), the electric field is weakly confined inside the absorber layer, resulting in limited absorption. In contrast, Fig. 6(i) (with SiO₂) shows strong field localization around the spheres and within the absorber, leading to a much higher light absorption. This difference is reflected in the absorbed power profiles shown in Fig. 6(f) (without SiO₂) and Fig. 6(l) (with SiO₂). Without SiO₂, the absorbed power at 825 nm is very low, while the addition of SiO₂ significantly boosts the absorbed power at this wavelength.

Fig. 6(m) provides a complete spectral evaluation of absorption (A), transmission (T), and reflection (R) in structures with and without SiO₂ nanospheres, covering the 300–827 nm range. The introduction of SiO₂ nanospheres leads to a consistent enhancement in absorption and suppression of optical losses across all wavelength regions. In the visible range (300–827 nm), the average absorption increases by 10.704%, rising from 0.715587 (without SiO₂) to 0.79218 (with SiO₂), primarily due to a 33.86% reduction in transmission and a 2.26% decrease in reflection. This improvement stems from the anti-reflective and light-scattering behaviour of the SiO₂ spheres, which promote more effective coupling of incident light into the absorber. These enhancements are achieved without altering the 300 nm active layer thickness, demonstrating that the SiO₂ nanosphere layer functions as a passive, low-loss photonic structure that improves light harvesting across the solar spectrum. Such a strategy offers a promising route to boost thin-film solar cell efficiency without compromising material simplicity or manufacturing scalability.

Fig. 7 presents the detailed electrical analysis of the perovskite solar cell, illustrating the impact of SiO₂ spheres on electron recombination, current density distribution, and overall device performance. Fig. 7(a–c) show the electron recombination rate at applied voltages of 0.03 V, 0.97 V, and 0.99 V, respectively. At low bias (0.03 V), recombination is minimal as the photogenerated carriers are efficiently extracted, maintaining a low recombination profile across the device. As the voltage increases to 0.97 V, close to the open-circuit condition, the recombination rate rises significantly, and at 0.99 V, recombination reaches its peak—corresponding to the point where the current output approaches zero, as confirmed by the J–V curve in Fig. 7(g).

Fig. 7. Analysis of recombination rate and electron current density in the perovskite solar cell: (a–c) electron recombination rate at applied voltages of 0.03 V, 0.97 V, and 0.99 V, respectively. (d–f) Electron current density distribution at 0.03 V, 0.97 V, and 0.99 V, respectively. (g) Comparison of the current density–voltage (J–V) characteristics and power–voltage (P–V) for devices with and without SiO₂ spheres.

Fig. 7(d–f) illustrate the electron current density distribution at the same voltage points. At 0.03 V, strong and uniform current flow is observed, indicating efficient carrier extraction under short-circuit conditions. As the applied voltage rises to 0.97 V, the current density gradually decreases due to enhanced recombination, and at 0.99 V, it falls close to zero, further confirming the loss of carrier extraction at high recombination conditions. Fig. 7(g) directly compares the J–V and P–V characteristics of the devices with and without SiO₂ spheres. The device incorporating SiO₂ spheres shows a substantial improvement in short-circuit current density, from 26.80 mA cm⁻² (without SiO₂) to 29.11 mA cm⁻² (with SiO₂), representing a ∼8.61% increase. Similarly, the pick power conversion efficiency (PCE) rises from 22.58% to 24.61%, reflecting an improvement of approximately ∼9% due to enhanced light absorption and improved carrier generation enabled by the SiO₂ spheres.

These numerical details are summarized in Table 2, which further highlights a very tiny change in the open-circuit voltage and fill factor, a 0.990 V to 0.995 V change for voltage and an 85.08% to 84.95% change for fill factor. Overall, this study demonstrates that embedding SiO₂ spheres significantly enhances both the optical and electrical performance of perovskite solar cells, enabling higher efficiency and stronger light harvesting even with a reduced absorber layer thickness, which also contributes to lowering material usage and potential lead-related environmental impact. By incorporating three SiO₂ spheres on top, PCE boosts significantly. This innovative enhancement takes performance to a whole new level.

Table 2. Comparison of photovoltaic performance parameters of perovskite solar cells with and without SiO₂ spheres.

Structure	E ff	J sc (mA cm−2)	V oc (V)	FF (%)
Without SiO2	22.58	26.80	0.990	85.08
With SiO2	24.61	29.11	0.995	84.95

To validate the feasibility of the obtained results, this study references data reported by A. M. Acevedo,³⁷ which outlines typical performance metrics for perovskite absorbers with a bandgap of approximately 1.5 eV. According to that report, such absorbers generally yield a short-circuit current density (J_sc) of around 29 ± 1 mA cm⁻², an open-circuit voltage (V_oc) of 1.2 ± 0.2 V, a fill factor (FF) of 89 ± 0.5%, and a power conversion efficiency (PCE) of approximately 31 ± 0.5%. These benchmarks provide a solid reference for evaluating simulation accuracy. In this study, a thinner MAPbI₃ absorber layer of only 300 nm was used—significantly less than the typical 1000–1500 nm range—to reduce lead (Pb) content and thus lower toxicity. Without any light-trapping structure, the simulated device yielded a PCE of 22.58%, a J_sc of 26.80 mA cm⁻², a V_oc of 0.99 V, and an FF of 85.08%, values that fall within the expected range, aside from the PCE which is naturally lower due to reduced absorption in the thinner layer. These results support the physical realism of the model.

To address the lower absorption, SiO₂ nanospheres were introduced as an external light-trapping structure. After optimizing their size, spacing, and embedding depth, the overall optical absorption increased by approximately 10.7%, primarily in the near-infrared region. This enhancement in light absorption led to a corresponding increase in short-circuit current density (J_sc) from 26.80 mA cm⁻² to 29.11 mA cm⁻², which represents an 8.6% improvement. Although the J_sc enhancement is slightly lower than the absorption gain, this is expected due to radiative and non-radiative recombination losses accounted for in the electrical simulation.

As a result of these improvements, the power conversion efficiency (PCE) rose from 22.58% to 24.61%, marking a 9% increase. While the open-circuit voltage (V_oc) and fill factor (FF) remained stable, the significant gains in absorption and carrier generation demonstrate the effectiveness of the SiO₂-based light-trapping strategy. This validates the strong coupling between enhanced optical performance and electrical output, even with a reduced absorber thickness. Also, this demonstrates that high-efficiency PSCs can be realized even with reduced absorber thickness, providing a scalable, cost-effective, and environmentally friendlier solution for future photovoltaic technologies.

3.3. Tolerance analysis of power conversion efficiency (PCE) and short-circuit current density (J_sc)

The performance of the proposed solar cell is affected by changes in some material properties, shown in Fig. 8. One of these is the permittivity (ε_r) of MAPbI₃, which is not fixed—it typically ranges from 5 to 7.^62,63 In this work, we used a value of 6.5, but during practical fabrication, it can vary within this range. To understand the impact, Fig. 8 shows how the power conversion efficiency (PCE) changes with different values of ε_r. The results show that the PCE can decrease from 24.607% to 24.586% (a drop of only 0.066%) if ε_r decreases from 6.5 to 5. On the other hand, if ε_r increases from 6.5 to 7, the PCE can slightly increase by 0.0063%. This indicates that changes in permittivity have a very small effect on the overall performance.

Fig. 8. Tolerance analysis of power conversion efficiency (PCE) and short-circuit current density (J_sc) under variations in permittivity (ε_r), doping concentration (N_A), carrier lifetime (τ), and carrier mobility (µ). (a) PCE uncertainty: varying permittivity ε_r (5–7) causes up to a +0.0063% and −0.066% change; a ±20% change in doping concentration (N_A) results in up to a +0.170% and −0.201% variation. (b) Short-circuit current density J_sc uncertainty: varying carrier lifetime τ (1 ns to 10 µs) causes up to +0.73% and −0.024% variation; varying carrier mobility µ (10–100 cm² V⁻¹ s⁻¹) causes up to +0.03% and −0.013% variation.

However, the doping concentration (N_A) also affects performance and can vary during fabrication. In our study, we considered a ±20% change in doping concentration. As a result, the PCE ranged from 24.406 to 24.777. A 20% decrease in doping concentration reduces the PCE by about 0.201%, while a 20% increase improves it by 0.170%. These variations are still within an acceptable range, meaning the proposed solar cell remains stable even with small changes in material properties.

In Fig. 8(b) illustrates the uncertainty analysis of the proposed model. In this test, the most influential electrical parameters affecting the short-circuit current density (J_sc) were varied, specifically, the carrier lifetime and carrier mobility. The carrier lifetime strongly depends on the synthesis quality of the perovskite layer; lower material quality introduces more defects, thereby reducing carrier lifetime, while improved processing and passivation enhance it. Typically, the carrier lifetime may vary from 1 ns to 10 µs. In this range, J_sc changes from 28.39 mA cm⁻² to 29.25 mA cm⁻². Another important parameter influencing J_sc is the carrier mobility, which can vary from 10 to 100 cm² V⁻¹ s⁻¹. Within this range, J_sc varies from 29.08 to 29.124 mA cm⁻².

The selection of an optimized 300 nm MAPbI₃ absorber layer represents a critical optoelectronic threshold that balances severe environmental vulnerabilities against hidden structural advantages. Because this thickness perfectly matches the material's native charge carrier diffusion length 100 nm to 300 nm, it provides exceptional bulk recombination resistance by allowing photogenerated carriers to be rapidly extracted before encountering deep traps, while its high mechanical compliance suppresses internal tensile stress and micro-cracking caused by thermal expansion mismatches with the substrate. However, this thin regime introduces distinct degradation liabilities: the reduced physical mass accelerates the penetration of atmospheric moisture (H₂O) and oxygen (O₂) that triggers chemical hydrolysis into yellow lead iodide (PbI₂), while solution-processing limits increase the risk of pinholes and grain boundary trenches that cause electrical shunting. Furthermore, the intense internal electric field under illumination aggravates volatile iodide ion (I⁻) migration, inducing current–voltage (J–V) hysteresis, and the shallow profile permits aggressive thermal outgassing of methylammonium (MA⁺) cations under operational heating up to 85 °C. Ultimately, the 300 nm configuration functions as an engineered equilibrium, balancing external atmospheric susceptibility against the substantial assets of internal mechanical flexibility and highly efficient, trap-free carrier transport.

4. Benchmarking with state-of-the-art perovskite solar cells

The performance of the proposed device was benchmarked against previously reported nanoparticle-enhanced perovskite solar cells, as summarized in Table 3. Several studies have demonstrated various nanostructure-based light management strategies to improve the power conversion efficiency (PCE) of perovskite solar cells (PSCs). For instance, ref. 35 introduced a SiO₂ prism-based light-trapping configuration in a SiO₂(prism)/ITO/PEDOT:PSS/PCDTBT/MAPbI₃/PC₆₀BM/Ag structure. Although this design achieved a high fill factor (FF) of 85.85%, the overall PCE remained at 21.16%, with a short-circuit current density (J_sc) of 23.47 mA cm⁻², indicating limited light absorption efficiency.

Table 3. Comparison of reported perovskite solar cell efficiencies enhanced by different nanoparticle (NP) approaches.

Ref.	Architecture of trapping mechanism	Trapping material	PCE (%)	J sc (mA cm−2)	V oc (V)	FF (%)
35	Metallic nanoparticle back-reflector	Au	21.16	23.47	1.05	85.85
64	Additive engineering	Additive only	19.19	23.95	1.15	70
65	Planer	No	18.48	22.64	1.06	77
66	Planer	No	17.51	22.36	1.05	75.42
68	Planer	No	14.85	21.17	1.10	63
69	Inverted pyramid textures	FTO and ETL	19.73	23.81	NA	NA
70	Interface engineering	Self material	16.35	21.43	0.998	74.6
74	Textured nanostructure	Silicon substrate and PDMS protective top-layer	18.29	22.28	0.98	83.13
75	Cylindrical surface	Absorber	20.19	24.50	NA	NA
This work	Nanosphere array	SiO2	24.61	29.11	0.995	84.95

In 2027, Wu et al.⁶⁴ employed additive engineering to enhance the thermal stability of MAPbI₃-based planar PSCs. Their device maintained stability for over 500 hours at 85 °C and achieved a PCE of 19.19% with a J_sc of 23.95 mA cm⁻². However, their planar structure and relatively thin (≈500 nm) absorber layer restricted further performance improvement. Similarly, Jia et al.⁶⁵ reported an 18.48% PCE using FAPbI₃ as a growth template for MAPbI₃, with a 2 µm-thick absorber layer. Despite their efforts to optimize growth via DFT analysis, such a thick film increases toxicity concerns and reduces carrier transport control during fabrication.

De Morais et al.⁶⁶ investigated the stability of air-processed MAPbI₃-based PSCs, achieving a PCE of 17.51%, a J_sc of 22.36 mA cm⁻², and a V_oc of 1.05 V. Although their process improved environmental stability, the device exhibited a relatively low FF (75.42%) and involved challenging fabrication control. Liu et al.⁶⁹ designed a light-trapping structure based on double inverted pyramids, which enhanced optical confinement but required highly precise fabrication to form sharp pyramid edges, making large-scale production difficult. Khadka et al.⁷⁰ analyzed perovskite degradation through thermal hysteresis of photocurrent, capacitance measurements, and SCAPS simulations. They found that device ageing increased thermally activated traps and interfacial ionic accumulation, leading to severe photocurrent loss. This highlights the importance of surface passivation to mitigate interfacial defects and improve device stability. Tooghi et al.⁷⁴ focused on optical parameter tuning via surface texturing; the merit of this approach is the significant enhancement of J_sc (from 17.51 to 22.28 mA cm⁻²) and an overall PCE boost to 18.29% achieved by minimizing surface reflection and maximizing light path length within the active layer. However, the demerit is that the texturing primarily yields optical improvements, leaving electronic parameters like V_oc (∼0.96 V) largely unimproved compared to the planar reference structure. In contrast, Fu et al.⁷⁵ explored a light-trapping approach using cylindrical MAPbI₃ microstructures. The merit of this design is an improved light absorption efficiency (93.86%) through scattering effects. The demerit, however, is a relatively lower PCE (20.19%) compared to advanced confinement strategies, likely due to the higher surface-to-volume ratio which can increase interface recombination.

Though in this work we focused on MAPbI₃ as the absorber because it is the most stable perovskite absorber. But recently perovskite research has also focused on developing lead-free materials and improving their optoelectronic performance.⁷¹ And significant progress has been made in this field based on energy conversion systems, though stability is a big issue that is limiting their application.^71,72

This work presents a novel light-trapping strategy by embedding a SiO₂ nanosphere array at the front surface of the perovskite solar cell (PSC), with each nanosphere positioned 50% inside the fluorine-doped tin oxide (FTO) layer and 50% exposed to air. As per our knowledge, this is the first time such a configuration has been introduced, offering a simple yet highly effective design that addresses multiple limitations in previous light management approaches. Unlike plasmonic nanoparticle-based methods, which involve complex fabrication, increased radiative and non-radiative recombination losses, higher series resistance, thermal degradation, and stability issues due to metallic inclusion within the absorber, this dielectric-based approach avoids these drawbacks entirely. Additionally, it resolves the complications of textured and complex surface structures (e.g., prism or star-shaped designs), which often induce surface defects, disturb absorber crystallinity, and present significant manufacturing challenges.⁷³

The proposed SiO₂ architecture is not only cost-effective and compatible with large-scale fabrication but also highly effective in enhancing absorption, achieving a 10.7% enhancement in total integrated absorption. Moreover, this strategy successfully mitigates the low power conversion efficiency (PCE) typically associated with thin absorbers by achieving a record-high PCE of 24.61% using only a 300 nm MAPbI₃ layer, surpassing the previously reported 24.5% from a much thicker 1110 nm planar absorber by A. A. B. Baloch et al.³⁸ This corresponds to a 73.78% reduction in absorber thickness and associated toxic lead (Pb) content, offering both environmental and cost advantages. The SiO₂ nanospheres lead to a 9.03% increase in PCE compared to the baseline (without nanospheres). Overall, this study introduces a scalable, low-cost, and high-performance light-trapping solution that advances the practicality, sustainability, and efficiency of perovskite solar cells.

5. Conclusion

In this work, a novel light-trapping strategy based on partially embedded SiO₂ nanospheres was proposed to enhance the performance of perovskite solar cells. The proposed configuration consists of three nanospheres on the top of the FTO with 50% embedded inside the FTO. This configuration significantly improves the performance of the solar cell; the PCE increases from 22.58% to 24.61%, while the J_sc increases from 26.80 to 29.11 mA cm⁻². Notably, these enhancements were achieved using a thin 300 nm absorber layer, reducing Pb content by 73.78%. This proposed approach offers a simple and effective pathway for improving the performance of PSC while supporting material reduction and environmental sustainability. Future work may focus on experimental validation and cost-effective optimisation.

It should be noted that this study is based on theoretical simulations under ideal conditions. So after fabrication, results may reduce because of imperfections, interface defects, and so on. So, future work may focus on experimental validation and cost-effective optimisation.

Author contributions

Conceptualization, Md Abu Huraiya, Abu S. M. Mohsin, Mohammed Belal and Md. Mosaddequr Rahman; data curation, formal analysis, investigation, Md Abu Huraiya, Abu S. M. Mohsin; resources, software, Md Abu Huraiya, Abu S. M. Mohsin; supervision, validation, Abu S. M. Mohsin, Mohammed Belal and Md. Mosaddequr Rahman; visualization, writing – original draft, Md Abu Huraiya; writing – review editing, Md Abu Huraiya, Abu S. M. Mohsin, Mohammed Belal and Md. Mosaddequr Rahman.

Conflicts of interest

No competing interests.

Data availability

Data will be made available on reasonable request from the corresponding author.