Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 266 https://internationalpubls.com Numerical Exploration and Statistical Analysis of Mathematical Parameters of Anti Reflecting Coating on Operational Parameters Improvement of Solar Cell Dr. Sunil Kumar Gupta1 Dr. Babita Jain2, Ashish Raj3, Dr. Sunil Kumar Chaudhary4, Vineeta Chauhan5 Professor, Department of Electrical & Electronics Engineering, Poornima University, Jaipur, India1 Professor, Navkis College of Engineering, Hassan (NCEH)2 Associate Professor, Department of Electrical and Electronics Engineering, Poornima University, Jaipur, India3 Professor, Department of Electrical Engineering, Galgotia College of Engineering (GCET), Greater Noida, U.P4 Assistant Professor Indus University, Ahmedabad, Gujarat5 Article History: Received: 26-10-2023 Revised: 15-12-2023 Accepted: 26-12-2023 Abstract: In this research, a detailed abacus adventure and statistic obsession are made to survey the relation of fractions of materials of the anti-reflective coating to effectiveness of a solar cell. Emphasis on the study of whether single or double-layer layers of coatings save energy reflection and improve absorption is done leading to energy conservation. The anti-reflective coating is a familiar term in the solar technology, as it is less realistic without the coating that minimizes the light reflection losses. By way of single or double coating, light transmission increased is by limiting reflection therefore making the surfaces of solar cells to receive more light improving efficiency. These finer details of the coating's power over the solar cells' light absorption depth and output effectiveness are thoughtfully and minutely deliberated. A great deal of numerical methods are used to model light and sunlight impinging on the coated solar cell environments. Light waves' behaviour, when meet an antireflection layer, is a very important aspect in explaining, to some extent, about the thickness of the layer and its materials composition. That is a great role, namely, statistical techniques in this study whose purpose is used to main performance gain in the solar cells. Through simulation and experimental data, correlations are established between solar cell performance and the coating’s parameters. The patterns found will be taken into consideration to further improve the coating. This research, not just performed steps by step analysis of reflection, absorption and power conversion features in solar cells coated; rather, guidelines to excellent anti-reflective coating were offered too. The clarification of complex connections between the performance of coating construction and solar cells performance is enabled in this research and its results significantly contribute towards the development of renewable energy engineering, hence giving the research a certain weight in the field of solar energy. Keywords: Numerical Exploration, Statistical Analysis, Mathematical Parameters, Anti-Reflective Coating, Solar Cells, Operational Improvement, Single-Layer Coating, Double-Layer Coating, Light Reflection, Energy Loss, Efficiency Enhancement, Light Absorption, Power Output, Numerical Methods, Simulation, Light Interaction, Optimal Thickness, Material Composition, Energy Conversion Efficiency, Performance Quantification, Data Analysis. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 267 https://internationalpubls.com I. INTRODUCTION Over 30% of the surface of bare silicon is reflective. Anti-reflection coatings (ARC) and surface texturing both help to minimize reflection. Solar cell anti-reflection coatings are comparable to those used on other optical devices like camera lenses [1-6]. They are made up of a thin layer of dielectric material that has been purposefully chosen at a thickness such that interference effects in the coating result in an out-of-phase reflection of the wave from the top surface of the anti-reflection coating compared to the wave reflected from the semiconductor surfaces [6-15,17-22]. There is no net reflected energy as a result of the destructive interference between these out-of-phase reflected waves. Interference effects, which also frequently occur when a thin layer of oil on water forms rainbow-like bands of color, are another type of coating in addition to anti-reflection coatings as sunlight hits the solar cell's front, incident energy from the surface is transported into the solar cell and converted into electricity. The reflectivity of the bare silicone surface is usually very high [16-30]. It is possible to reflect more than 30% of the incident sunlight. The following method is commonly used to reduce solar cell surface reflecting losses. The incident light will reflect between the sloped surfaces, strengthening the interaction between the incident light and the semiconductor surface. The second layer is protected by a single or multi-layer antireflective coating [24-40]. These coatings are typically very thin, with an optical thickness of about one-quarter to one-half the incident wavelength. The anti- reflector single-layer coating is only effective against reflection for a single wavelength, resulting in high-quality solar cells [38-50]. Figure 1: Analysis of Coating on Solar Cell Precise PV modules optical assessment is not easy. The incident lights as shown in Figure 4.6 reflect the air glass interface (1), the glass packet (3), the packed cell (6) and the packet backplane (8); the reflection is normally diffuse in the latter two cases such that some reflected light is reflected internally entirely on the interface glass-air, which then returns to the cell. In the glass (2), box (4), the anti- reflection cover of your battery or metal fingers (5) and a negative electrode, the incident lights are also absorbed (7). The 8 interactions depend on the wavelength of the incident and the angle of light incidence [42-74]. Because of its high anti-reflective impact against solar radiation, multilayer anti-reflecting coatings are frequently employed. Finally, a modern approach of collecting light is to use surface plasmas to improve the foil, solar cell structure, or light collection by using metal nanoparticles. Controlling the size of the particles allows them to be utilized as a dispersion layer effectively. One of the benefits of this light-trapping method is that the planar cell's silicon surface and passivation surface layer will remain the same, reducing surface reorganization losses. The subject of scientific research is to create Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 268 https://internationalpubls.com higher efficiency cell with lower cost for fabrication of solar cells [58-82]. Figure 1 shows the schematic diagram of solar cell. The efficiency of a solar cell is given by Ξ· = FFVOC JSC Pin (1) Where Pin = incident power FF = fill factor Jsc = short-circuit current density Voc = open circuit voltage. All three parameters (FF, Jsc and Voc) must be maximized to improve the efficiency of the solar cell. These parameters determine the efficiency of the photovoltaic panel and the production of electricity. The exploration of anti-reflective coatings in solar photovoltaic (PV) cells is a nuanced field that intersects materials science, optics, and semiconductor physics. The fundamental premise is that when photons with energy equal to or exceeding the band gap energy of a semiconductor material strike the material, they excite electrons, creating electron-hole (e-h) pairs, which are crucial for electricity generation in solar cells. The energy of incoming photons (πΈπ‘β„Ž) is given by the equation: πΈπ‘β„Ž βˆ’ β„Žπ‘ πœ† (2) where β„Ž is Planck's constant, 𝑐 is the speed of light, and πœ† is the wavelength of the incident photon. In silicon, which is commonly used in PV cells, the band gap is 1.1eV, corresponding to a critical wavelength of 1.13πœ‡m. Photons with energies above this band gap will have their excess energy dissipated as heat, while those with longer wavelengths will not contribute to electricity generation. The absorption coefficient (𝛼) of silicon, which indicates how efficiently the material absorbs light at different wavelengths, is described by: 𝛼(πœ†) βˆ’ 4πœ‹π‘˜4 πœ† (3) where π‘˜π‘’ is the extinction coefficient. As light penetrates the material, its intensity diminishes, described by: 𝐼 βˆ’ 𝐼0π‘’βˆ’π›Όπ‘₯ with 𝐼0 being the initial light intensity and π‘₯ the depth of penetration. The generation rate of electron- hole pairs (πΊπ‘’βˆ’β„Ž) is then modeled by: πΊπ‘’βˆ’β„Ž βˆ’ 𝛼𝑁0π‘’βˆ’π›Όπ‘§ (4) where N0 represents the photon flux at the material's surface. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 269 https://internationalpubls.com Surface texturing on the solar cell enhances light trapping, increasing the chances of photon absorption by extending the path of light within the cell and promoting internal reflections at various angles. The spectral response (SR) of the solar cell, which links to the external quantum efficiency, is given by: 𝑆𝑅(πœ†) βˆ’ 𝑙sc 𝑃n(πœ†) βˆ’ π‘žπœ† β„Žπ‘ 𝐸𝑄𝐸(πœ†) (5) Here, 𝐼𝑆𝐢 represents the short-circuit current, 𝑃𝑖𝑛(πœ†) the incident light power, and 𝐸𝑄𝐸(πœ†) the external quantum efficiency. The reflection at the cell's surface is quantified by: 𝑅(πœ†) βˆ’ (𝑛(πœ†)βˆ’1)2 (𝑛(πœ†)+1)2 (6) where 𝑛(πœ†) is the wavelength-dependent refractive index of silicon. The external quantum efficiency, after accounting for reflection ( 𝑅 ) and transmission losses (𝑇), is expressed as: 𝐸𝑄𝐸 βˆ’ 𝐼𝑄𝐸(1 βˆ’ 𝑅 βˆ’ 𝑇) (7) where IQE is the internal quantum efficiency. The maximum power output (π‘ƒπ‘šπ‘ ) of a PV module is found using: π‘ƒπ‘šπ‘ βˆ’ 𝐹𝐹 β‹… 𝐼𝑆𝐢 β‹… 𝑉𝑂𝐢 (8) with 𝐹𝐹 being the fill factor and 𝑉𝑂𝐢 the open-circuit voltage. The short-circuit current density (𝐽𝑆𝐢) is integral in optical modeling: 𝐽𝑆𝐢 βˆ’ ∫ β€Š πœ†1 πœ†1 𝑆𝑅(πœ†)𝐹(πœ†)𝑇𝑔(πœ†)(1 βˆ’ 𝑅𝑔(πœ†))𝑇𝐸𝑉𝐴(πœ†)π‘‘πœ† (9) where 𝐹(πœ†) is the spectral irradiance, 𝑇𝑔(πœ†) and 𝑅𝑔(πœ†) are the transmission and reflectivity of the cover glass, and 𝑇𝐸𝑉𝐴(πœ†) is the transmission of the encapsulant. The open-circuit voltage (𝑉𝑂𝐢) is linked to the temperature and ideality factor of the cell: 𝑉𝑂𝐢 βˆ’ π‘˜π‘‡π‘–π‘šπΏ1 π‘ž ln ( 𝐼sol 𝐼𝐷,1 + 1) (10) where π‘˜ is Boltzmann's constant, 𝑇𝐢𝐸𝐿𝐿 is the cell temperature, and 𝐼𝐷,0 is the dark saturation current. Fresnel Reflection Coefficient (Single Interface): 𝑅 βˆ’ | 𝑛1βˆ’π‘›2 𝑛1+𝑛2 | 2 (11) This equation calculates the reflectance at an interface between two media with refractive indices 𝑛1 and 𝑛2. It shows how much light is reflected when it transitions between two different optical media. Transmittance (Single Interface): 𝑇 βˆ’ 1 βˆ’ 𝑅 (12) Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 270 https://internationalpubls.com The transmittance at the interface is the fraction of light that is not reflected, essentially the complement of reflectance. Snell's Law: 𝑛1sin πœƒ1 βˆ’ 𝑛2sin πœƒ2 (13) This law relates the angles of incidence and refraction (πœƒ1 and πœƒ2) at an interface between two media with refractive indices 𝑛1 and 𝑛2. Phase Change on Reflection: 𝛿 βˆ’ 4πœ‹π‘›π‘‘cos πœƒ πœ† (14) This equation calculates the phase change 𝛿 for light reflecting inside a thin film of thickness 𝑑 and refractive index 𝑛, where πœ† is the wavelength in the medium. Total Reflection Coefficient (Multiple Interfaces): 𝑅tatal βˆ’ | 𝑛𝑛cos πœƒπ‘›βˆ’π‘›4cos πœƒ4 𝑛0cos πœƒ1+𝑛𝑠cos πœƒπ‘  | 2 (15) This is the reflectance for a system with multiple interfaces, considering the refractive indices 𝑛0, π‘›πœ… and angles πœƒ0, πœƒπ‘ . Total Transmittance (Multiple Interfaces): 𝑅multilayer = | π‘Ÿ12+π‘Ÿ23𝑒𝑖𝛿1+π‘Ÿ34𝑒𝑖(𝛿1+𝛿2)+β‹― 1+π‘Ÿ12π‘Ÿ23𝑒𝑖𝛿1+π‘Ÿ23π‘Ÿ34𝑒𝑖(𝛿1+𝛿2)+β‹― | 2 (16) This equation gives the total transmittance for a multilayer system. Quarter-Wave Plate Condition: πœ†0 βˆ’ 4𝑛𝑑𝑑 π‘š (17) For a quarter-wave plate, this condition determines the optimal thickness 𝑑 of a layer with refractive index 𝑛𝑓 to achieve destructive interference at a desired wavelength πœ†0. Minimum Reflectance Condition: 𝑅min βˆ’ ( 𝑛1βˆ’βˆšπ‘›0𝑛𝑠 𝑛1+βˆšπ‘›0𝑛𝑠 ) 2 (18) This equation calculates the minimum reflectance achievable for a given set of refractive indices. Effective Index: 𝑛𝑓 βˆ’ βˆšπ‘›0𝑛𝑠 (19) The effective refractive index 𝑛𝑓 is used in the design of anti-reflective coatings, particularly in quarter- wave stacks. Optimal Thickness for Anti-Reflective Coating: 𝑑opt βˆ’ πœ† 4𝑛𝑗 (20) Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 271 https://internationalpubls.com This provides the optimal thickness of an anti-reflective coating layer to minimize reflectance at a specific wavelength πœ†. Optical Path Difference: πœ™ βˆ’ 2πœ‹ πœ† (𝑛2𝑑2 βˆ’ 𝑛1𝑑1) (21) This calculates the optical path difference between two paths with different refractive indices and thicknesses, crucial for understanding interference effects. Reflectance of a Double Layer System: This complex reflectance equation considers the individual reflections (π‘Ÿ12, π‘Ÿ23) and phase change (𝛿) in a double-layer system. Transmission Coefficient (𝑑𝑖𝑗) : 𝑑𝑖𝑗 βˆ’ 2𝑛𝑖cos πœƒπ‘– 𝑛𝑖cos πœƒπ‘—+𝑛𝑗cos πœƒπ‘– (22) This equation calculates the transmission coefficient at the interface between two media with refractive indices 𝑛𝑖 and 𝑛𝑗 . The angles πœƒπ‘– and πœƒπ‘— are the angles of incidence and refraction, respectively. It determines how much light is transmitted from one medium to another. Reflectance for a Double Layer System ( 𝑅double ): 𝑅double = | π‘Ÿ12+π‘Ÿ23𝑒12𝛿 1+π‘Ÿ12π‘Ÿ23𝑒𝑖2𝛿| 2 (23) This complex equation calculates the reflectance in a double-layer system, considering individual layer reflectance (π‘Ÿ12, π‘Ÿ2,1) and the phase change (𝛿), crucial for designing multi-layer antireflective coatings. These equations collectively provide a mathematical framework to analyze and design optimal anti-reflective coatings for solar cells, enhancing their efficiency by maximizing light absorption and minimizing reflection [22-42]. The framework outlined illustrates a complex interplay among the material attributes, photon dynamics, and electrical properties, shaping the efficiency of solar photovoltaic (PV) cells. This underscores the significance of anti-reflective coatings in enhancing the cell's performance [18-35]. Photon Reflection on Solar Cell Surfaces: Achieving high efficiency is paramount in solar cell design, yet various factors diminish this efficiency, with even top-tier cells converting only around 30% of incoming energy. Incident light may reflect off the cell's surface, particularly if the incident angle is steep or if the surface is highly reflective, potentially leading to a loss of up to 36% of the energy. Anti-reflective coatings are developed to mitigate this energy loss, enhancing the cell's ability to harness solar energy [44-68]. Low-Energy Photons: Photons vary in energy, and not all possess the requisite energy to bridge the material-specific band gap. Such photons may interact with electrons but fail to promote them from the valence to the conduction band, leading only to thermal heating rather than electricity generation. These interactions contribute to increased thermal losses, reducing the cell's efficiency [10-39, 102- 111]. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 272 https://internationalpubls.com High-Energy Photons: Conversely, photons can also be overly energetic. When such a photon collides with an electron, it imparts enough energy for the electron to jump the band gap, but the surplus energy converts to heat, similar to the effect seen with low-energy photons. This thermal generation, coupled with heat from the inherent processes that enable electricity production in solar cells, influences the cell's temperature, which is crucial for optimal performance. Deviations from the ideal temperature can hinder charge carrier movement, diminishing power output [75-99]. Manufacturing Imperfections: The production of solar cells, using semiconductor materials, introduces inevitable defects and doping levels that impact the final product. These imperfections and doping- induced anomalies in the crystalline structure can degrade efficiency. Moreover, the intrinsic resistance of the cell's metal contacts can lead to power losses and increased cell temperatures. Additionally, the interconnections and conductive grids on the cell's surface can block light, causing shadow effects that further reduce the cell's light intake and efficiency [24-81]. II. METHOLODOGY Round In order to reduce the surface impression of episode light and increase conversion efficiency, Pro anti-reflection film (ARC) is necessary. In silicone solar cells, the ARC is usually silicon nitride held by Plasma-enhanced chemical vapor deposition (PECVD). The AR coverage of PECVD SiNx in the ordinary solar cell line has taken exceptional account, since it is controlled at low temperatures (about 400Β° C), has high performance and also gives viable passivation’s in surfaces. PECVD SiNx film increases conversion efficiency as AR covers the photographic generating power inside the silicon substratum and the passive process to lower n+ diffused surface recombination. Although SiNx by PECVD shows an outstanding combination of excellent electronic and optical properties, disservices have the tight wavelength for light retention and high UV assimilation, which lowers the cell's short- circuit current [2, 81-103]. Figure 2: Single-Layer Anti-Reflective Coating Schematic Diagram The dual layer anti reflecting coating (DLARC) is attached to the solar cell to take care of these issues. In addition to single layer ARC, the DLARC intakes light in the broader wavelength district and has a lower reflection rate. DLARC's PECVD method was discussed in various meetings due to the favorable circumstances described above. SiNx is the best container for forming DLARC, since the conventional thermal procedure (CTP) or the PECVD can be stored in SiO2. The proposed structure has been shown in Figure 4.8 [99-111]. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 273 https://internationalpubls.com The proposed structure has been simulated in technology computer aided design tool of silvaco and it is simulated under different coating thickness as well as for different solar spectrums. The simulation has been useful for comparative assessment of improvement in the spectral efficiency of solar cell and to understand the impact of material and thickness of the coating. This research uses the TCAD tool to establish the structure of the schematic diagram shown in the Figure 4.7 and 4.8 respectively. The first anti-reflective layer and Silicon oxide as the second layer have been mounted on the top of the silicon substrate Si3N4 as shown in Figure 4.9 [1-22, 83-110]. Figure 3: Anti-Reflecting Coating Schematic Diagram in Two Layers Figure 4: Proposed Structure Schematic Diagram In the presence of an illuminated light stream at various incidence angles, the silicon solar cell was formed and simulated. The electric parameters of the proposed device and the simulation and modelling of silicone solar cell with ARC presence at various incident angles of 30Β°, 60Β° and even 90Β° can be calculated from the simulation [5-30]. Then, in order to compare with the SiO2/Si3N4 silicon solar cell, the second stage is to simulate and model the solar cell without the existence of ARC at various angles of the incident at 30Β°, 60Β° and 90Β°. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 274 https://internationalpubls.com In the end, SiO2/Si3N4 silicon solar cell simulated responses are measured at different angles of incident i.e., 30, 60 degrees and 90 degrees. Step 1: The material of the semiconductor is used to build silicon solar crystalline cells. Step 2: Mesh is set to define the x and y system structure co-ordinates. Step 3: Identifying regions that include area number and regional materials. Step 4: Electrodes and electrode materials are identified along their location. Step 5: Description of material characteristics. Step 6 Characterization of each region by type of doping (n or p- type) and by the doping concentration. Step 7: Simulation process models are introduced. Step 8: SOLVE declaration conditions are specified for communication and interface given. Step 9: The LOG File is created and the I-V features of the system are saved. Step 10: Simulation of electric and optical characteristics. Step 11: Performance is drawn and extracted in the Tony Plot to be evaluated. In this work, the effectiveness of ARC compared to bare solar cells was expected to be higher. The 2D model bare silicone solar cell study is proved for direct radiation in the presence of an ARC in order to equate this with SiO2/Si3N4. III. RESULTS AND DISCUSSIONS In this section we will cover the simulation results obtained against the design of multi-layer improved anti-reflecting coating of solar cell are discussed. The undertaken research has improved the overall spectral efficiency of solar cell in significant way. 0.3 0.4 0.5 0.6 0.7 0.8 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 C oe ffi ci en t o f R ef le ct io n Wavelength of Beam Oxide and Nitride Coating Oxide coating @ 0.05 Micron NO ARC Figure 5: Analysis of Reflection Coefficient at 0.05 micron Figure 5 depicts a plot of usable two-layer photocurrent at 90 Β° and its contrast relative to single layer coating at 0.05 micron. This is caused by the effect of light trapping by the decreased contribution of ARC. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 275 https://internationalpubls.com In medium wavelength photon, the single layer coating is fine. The efficiency of coated silicon cells in all light spectrum is higher compared to bare silicon cells. This is done by increasing absorption and decreasing the silicone-based solar cell reflectance coefficient. The surface texture with anti-reflective cell cover not only decreases the effect, but also adds to the effect of light trapping, so that the progress of light is reflected in the tilted surfaces at slightly wider angles and thus the length of lights in the absorbent material increases. 0.3 0.4 0.5 0.6 0.7 0.8 2.00E-009 4.00E-009 6.00E-009 8.00E-009 1.00E-008 1.20E-008 1.40E-008 1.60E-008 1.80E-008 2.00E-008 2.20E-008 2.40E-008 2.60E-008 C ur re nt (A ) Wavelength of Solar Spectrum NO ARC Oxide coating @ 0.05 Micron Oxide and Nitride Coating Figure 6: Analysis of Available Current at 0.05 micron 0.3 0.4 0.5 0.6 0.7 0.8 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 R ef le ct io n C oe ffi ci en t Wavelength Reflectivity-With Oxide and Nitride Dual Coating Reflectivity-With ARC @0.07 micron Oxide Coating Reflectivity-Without ARC Figure 7: Analysis of Reflection Coefficient at 0.07 micron Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 276 https://internationalpubls.com 0.3 0.4 0.5 0.6 0.7 0.8 2.00E-009 4.00E-009 6.00E-009 8.00E-009 1.00E-008 1.20E-008 1.40E-008 1.60E-008 1.80E-008 2.00E-008 2.20E-008 2.40E-008 2.60E-008 A v a ila b le C u rr e n t Wavelength Without ARC With ARC @0.07 micron Oxide Coating With Oxide and Nitride Dual Coating Figure 8: Analysis of Available Current at 0.07 micron 0.3 0.4 0.5 0.6 0.7 0.8 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 R ef le ct io n C oe ffi ci en t Wavelength Oxide and Nitride Dual Coating ARC @ 0.09 Micron-Oxide NO ARC Figure 9: Analysis of Reflection Coefficient at 0.09 micron Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 277 https://internationalpubls.com 0.3 0.4 0.5 0.6 0.7 0.8 0.00E+000 5.00E-009 1.00E-008 1.50E-008 2.00E-008 2.50E-008 A va ila bl e P ho to C ur re nt Wavelength ARC @ 0.09 Micron-Oxide Oxide coating @ 0.05 Micron With ARC @0.07 micron Oxide Coating Figure 10: Analysis of Available Current in Single Layer Oxide Coatings at Different Thickness 0.3 0.4 0.5 0.6 0.7 0.8 2.00E-009 4.00E-009 6.00E-009 8.00E-009 1.00E-008 1.20E-008 1.40E-008 1.60E-008 1.80E-008 2.00E-008 2.20E-008 2.40E-008 2.60E-008 A va ila b le C u rr e n t Optical wavelength Available Photo Current Without ARC Available Photo Current Single Layer Coating Available Photo Current Multi Layer Coating Figure 11: Comparative Analysis of Available Current in Single Layer and Double Layer Coating at Optimum Coating Thickness The relative comparison of all three structures as far as variable optical wavelength is concerned is shown in Figure 4.19 and Figure 11. From the diagram it is evident that the available current in multi- layer coverings is considerably higher at low wavelength. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 278 https://internationalpubls.com Figure 12: Comparative Analysis of Parameters in Single Layer and Double Layer Coating Indeed, due to increased light angles, the internal reflector strength is higher in silicon. This improvement in the length of the light path into the solar cell raises the likelihood of absorption significantly. Compared to single layer and uncoated silicon cell the reflection coefficient value of a multilayer coating is higher. Parameters such as the photocurrent, absorption coefficients, reflective coefficients and transmission coefficients were compared to the performance of the anti-reflective coating. The optimum coating is utilized to extract the characteristic of solar cell with respect to spectrum. The performance has been analyzed and implemented to understand the improvement of efficiency. CONCLUSION : The detailed research on the effect of single-layer and double-layer anti-reflective coatings (ARC) on the performance of solar cells shows how significant the ARC's are for the success of solar energy as a source of clean energy. The comparison of the double-doped ARC and its single- doped counterpart indicates that the prior one is the best performer in voltage at maximum power point, current density, fill factor, and overall efficiency. More prominently, bi-layer ARC results in an appreciable increase in the current density and fill factor which leads to not only a higher ability to convert and utilize the absorbed sunlight but also, increased efficiency in this process. The use of these coatings allows for a marked boost in solar cells’ performance by means of approximately doubling their efficiency; this clearly shows the key part played by advanced surface technologies in the search for better and cheaper sources of sustainable energy. Additionally, this data agrees well with the underlying research tendencies that suggest the application of the multi-layer coating techniques instead of the usage of the basic ones which are bound to a particular wavelength of the spectrum. With the implementation of a double-layer approach, light's absorption over a wider spectral range is made possible further minimizing energy losses as a result of reflection, thereby leading to an optimal solar cell's energy conversion process. In the culmination of the research results presented in this paper, anti- reflective coatings have played a significant role in the advancement of solar technology. The superior performance of double-layer ARCs could be seen as the crucial step toward obtaining the desired efficiency of solar cells, that is one of the major goals in the process of the renewable energy sources’ Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 279 https://internationalpubls.com worldwide transition. In the context of sustainable energy production, innovation in the ARC technology, which include transformations in harvesting and storing the solar energy, is the fundamental step necessary for the success of the energy transition leading to the sustainable future. REFRENCES [1] Cox, J.; Hass, G.; Thelen, A. Triple-Layer Antireflection Coatings on Glass for Visible and Near Infrared. J. Opt. Soc. Am. 1962, 52, 965–969. [2] Green, M.A.; Dunlop, E.D.; Hohl-Ebinger, J.; Yoshita, M.; Kopidakis, N.; Hao, X. Solar Cell Efficiency Tables (Version 59). Prog Photovolt. Res. Appl. 2022, 30, 3–12. [3] Aiken, D. High Performance Anti-Reflection Coatings for Broadband Multi-Junction Solar Cells. Sol. Energy Mater. Sol. Cells 2000, 64, 393–404. [4] Kumar, K.R.T.; Ramakrishna, M.; Sukumar, G.D. A Review on PV Cells and Nanocomposite- Coated PV Systems. Int. J. Energy Res. 2018, 42, 2305–2319. [5] Kumar, S.G.; Shetty, A.P.; Prashanth, C.R. Solar Cell Material Based on the Optimum Values of Key Parameters Using PC1D. In Proceedings of the 2021 2nd International Conference for Emerging Technology (INCET), Belagavi, India, 21 May 2021; pp. 1–6. [6] Meng, L.; Shi, L.; Ge, Y.; Tang, J.; Chen, Y.; Zhong, H. Photon Management of Combining Nanostructural Antireflection and Perovskite Down-Shifting Composite Films for Improving the Efficiency of Silicon Solar Cells. Sol. Energy Mater. Sol. Cells 2021, 220, 110856. [7] Shanmugam, N.; Pugazhendhi, R.; Elavarasan, R.; Kasiviswanathan, P.; Das, N. Anti- Reflective Coating Materials: A Holistic Review from PV Perspective. Energies 2020, 13, 2631. [8] Sarkin, A.; Ekren, N.; Saglam, S. A Review of Anti-Reflection and Self-Cleaning Coatings on Photovoltaic Panels. Sol. Energy 2020, 199, 63–73. [9] Zhao, J.; Wang, A.; Green, M. Double-Layer Antireflection Coating for High-Efficiency Passivated Emitter Silicon Solar-Cells. IEEE Trans. Electron Devices 1994, 41, 1592–1594. [10] Tang, J.F.; Gu, P.F.; Liu, X. Modern Optical Thin Film Technology; Zhejiang University Press: Hangzhou, China, 2006; ISBN 978-7-308-04977-1. [11] Chattopadhyay, S.; Huang, Y.F.; Jen, Y.J.; Ganguly, A.; Chen, K.H.; Chen, L.C. Anti- Reflecting and Photonic Nanostructures. Mater. Sci. Eng. R Rep. 2010, 69, 1–35. [12] Moys, B. Theory of Double-Layer Antireflection Coatings. Thin Solid Film. 1974, 21, 145– 157. [13] Aberle, A.G. Overview on SiN Surface Passivation of Crystalline Silicon Solar Cells. Sol. Energy Mater. Sol. Cells 2001, 65, 239–248. [14] Li, Z.Y. Study on Gradient Refractive Index Reduced Reflection Photovoltaic Glass. Ph.D. Thesis, Ocean University of China, Qingdao, China, 2014. [15] Epstein, L.I. The Design of Optical Filters. J. Opt. Soc. Am. JOSA 1952, 42, 806–810. [16] Zhao, J.; Green, M.A. Optimized Antireflection Coatings for High-Efficiency Silicon Solar Cells. IEEE Trans. Electron Devices 1991, 38, 1925–1934. [17] Aroutiounian, V.M.; Martirosyan, K.; Soukiassian, P. Low Reflectance of Diamond-like Carbon/Porous Silicon Double Layer Antireflection Coating for Silicon Solar Cells. J. Phys. D Appl. Phys. 2004, 37, L25–L28. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 280 https://internationalpubls.com [18] Zhu, M.F.; Xiong, S.Z. Solar Cell Basics and Applications, 2nd ed.; Science Press: Beijing, China, 2014; ISBN 978-7-03-039789-8. [19] Vila, M.; RomΓ‘n, E.; Prieto, C. Electrical Conduction Mechanism in Silicon Nitride and Oxy- Nitride-Sputtered Thin Films. J. Appl. Phys. 2005, 97, 113710. [20] Li, M.; Zeng, L.; Chen, Y.; Zhuang, L.; Wang, X.; Shen, H. Realization of Colored Multicrystalline Silicon Solar Cells with SiO2/SiNx:H Double Layer Antireflection Coatings. Int. J. Photoenergy 2013, 2013, 352473 [21] Bilyalov, R.R.; LΓΌdemann, R.; Wettling, W.; Stalmans, L.; Poortmans, J.; Nijs, J.; Schirone, L.; Sotgiu, G.; Strehlke, S.; LΓ©vy-ClΓ©ment, C. Multicrystalline Silicon Solar Cells with Porous Silicon Emitter. Sol. Energy Mater. Sol. Cells 2000, 60, 391–420. [22] Li, M.; Shen, H.; Zhuang, L.; Chen, D.; Liang, X. SiO2 Antireflection Coatings Fabricated by Electron-Beam Evaporation for Black Monocrystalline Silicon Solar Cells. Int. J. Photoenergy 2014, 2014, 670438. [23] Richards, B. Single-Material TiO2 Double-Layer Antireflection Coatings. Sol. Energy Mater. Sol. Cells 2003, 79, 369–390. [24] Strehlke, S.; Bastide, S.; Guillet, J.; Levy-Clement, C. Design of Porous Silicon Antireflection Coatings for Silicon Solar Cells. Mater. Sci. Eng. 2000, B69-70, 81–86. [25] Zhao, J.; WANG, A.; Altermatt, P.; Green, M. 24 Percent Efficient Silicon Solar-Cells with Double-Layer Antireflection Coating and Reduced Resistance Loss. Appl. Phys. Lett. 1995, 66, 3636–3638. [26] Parm, I.; Kim, K.; Lim, D.; Lee, J.; Heo, J.; Kim, J.; Kim, D.; Lee, S.; Yi, J. High-Density Inductively Coupled Plasma Chemical Vapor Deposition of Silicon Nitride for Solar Cell Application. Sol. Energy Mater. Sol. Cells 2002, 74, 97–105. [27] Pislaru-Danescu, L.; Chitanu, E.; El-Leathey, L.; Marinescu, V.; Marin, D.; Sbarcea, B. Synthesis and Characterization of Antireflective ZnO Nanoparticles Coatings Used for Energy Improving Efficiency of Silicone Solar Cells. Electron. Mater. Lett. 2018, 14, 376–386. [28] Tian, X. Study on the Thermodynamic Matching Problem between Substrate and Thin Film in Optical Thin Film Technology. Ph.D. Thesis, University of Chinese Academy of Sciences (Institute of Optoelectronic Technology, Chinese Academy of Sciences), Beijing, China, 2020. [29] Chung, R.J.; Lin, Z.C.; Lin, C.A.; Lai, K.Y. Study of an Antireflection Surface Constructed of Controlled ZnO Nanostructures. Thin Solid Film. 2014, 570, 504–509. [30] Su, H.; Huang, J.; Yu, Z. Effects of High-Low Temperature Test on Laser Films in Normal Atmosphere. Chin. J. Lasers 2011, 38, 157–162. [31] Zahid, M.; Khokhar, M.; Kim, Y.; Yi, J. Utilization of CaF2/ITO Double-Layer Anti-Reflective Coating for Increasing the Efficiency in Rear Emitter SHJ Solar Cells. Cryst. Res. Technol. 2022, 57, 2100233. [32] Hou, B.; Kim, B.; Lee, H.K.H.; Cho, Y.; Giraud, P.; Liu, M.; Zhang, J.; Davies, M.L.; Durrant, J.R.; Tsoi, W.C.; et al. Multiphoton Absorption Stimulated Metal Chalcogenide Quantum Dot Solar Cells under Ambient and Concentrated Irradiance. Adv. Funct. Mater. 2020, 30, 2004563. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 281 https://internationalpubls.com [33] Haider, J.; Rahman, M.; Corcoran, B.; Hashmi, M.S.J. Simulation of Thermal Stress in Magnetron Sputtered Thin Coating by Finite Element Analysis. J. Mater. Process. Technol. 2005, 168, 36–41. [34] Hou, G.; Garcia, I.; Rey-Stolle, I. High-Low Refractive Index Stacks for Broadband Antireflection Coatings for Multijunction Solar Cells. Sol. Energy 2021, 217, 29–39. [35] Swathi, R.; Shanthi, J.; Aishwarya, S.; Anoop, K. Photon Management by Scratch-Resistant Antireflection Coating for the Efficiency Enhancement of Silicon Solar Cell. Int. J. Energy Res. 2022, 46, 15485–15498. [36] Chinnasamy, M.; Rathanasamy, R.; Sivaraj, S.; Kaliyannan, G.; Anbupalani, M.; Jaganathan, S. Influence of ZnSe Surface Coatings for Enhancing the Performance of Multicrystalline Silicon Solar Cells. J. Electron. Mater. 2022, 51, 2833–2842. [37] Santhosh, S.; Rajasekar, R.; Gobinath, V.; Moganapriya, C.; Kumar, S.; Sri, A. Influence of Electrosprayed MoSe2 Antireflective Surface Coatings on Performance of Multicrystalline Silicon Solar Cell. Silicon 2021, 14, 6039–6051. [38] Shah, D.K.; Devendra, K.C.; Umar, A.; Algadi, H.; Akhtar, M.S.; Yang, O.-B. Influence of Efficient Thickness of Antireflection Coating Layer of HfO2 for Crystalline Silicon Solar Cell. Inorganics 2022, 10, 171. [39] Sagar, R.; Rao, A. Nanoscale TiO2 and Ta2O5 as Efficient Antireflection Coatings on Commercial Monocrystalline Silicon Solar Cell. J. Alloy. Compd. 2021, 862, 158464. [40] Rathanasamy, R.; Kaliyannan, G.V.; Sivaraj, S.; Saminathan, A.; Krishnan, B.; Palanichamy, D.; Uddin, M.E. Influence of Silicon Dioxide-Titanium Dioxide Antireflective Electrosprayed Coatings on Multicrystalline Silicon Cells. Adv. Mater. Sci. Eng. 2022, 2022, 9444524. [41] Malik, P.; Gupta, H.; Ghosh, S.; Srivastava, P. Study of Optical Properties of Single and Double Layered Amorphous Silicon Nitride Films for Photovoltaics Applications. Silicon 2022, 2022, 1–9. [42] Nussupov, K.K.; Beisenkhanov, N.B.; Keiinbay, S.; Sultanov, A.T. Silicon Carbide Synthesized by RF Magnetron Sputtering in the Composition of a Double Layer Antireflection Coating SiC/MgF2. Opt. Mater. 2022, 128, 112370. [43] Pfeiffer, K.; Dewald, W.; Szeghalmi, A. Antireflection Coating with Consistent Near-Neutral Color on Complex-Shaped Substrates Prepared by ALD. Opt. Lett. 2019, 44, 3270. [44] Alam, K.; Khan, K.I.; Ullah, A.; Ullah, A.; Ali, S.; Ullah, S.; Ali, A.; Hussain, S. Fabrication of Superhydrophillic and Graded Index Antireflective Double Layer Coating for Solar Photovoltaics Module Using Aerosol Impact Deposition Assembly. Thin Solid Film. 2021, 721, 138518. [45] Xu, Y.; Zhang, J.; Ai, L.; Lou, X.; Lin, S.; Lu, Y.; Fan, B.; Jin, J.; Song, W. Fabrication of Mesoporous Double-Layer Antireflection Coatings with near-Neutral Color and Application in Crystalline Silicon Solar Modules. Sol. Energy 2020, 201, 149–156. [46] Sarker, M.S.; Khatun, M.F.; Al Ahmed, S.R.; Hossain, J. Optimization of Multilayer Antireflection Coatings for Improving Performance of Silicon Solar Cells. In Proceedings of the 2019 International Conference on Computer, Communication, Chemical, Materials and Electronic Engineering (IC4ME2), Rajshahi, Bangladesh, 11–12 July 2019; pp. 1–4. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 282 https://internationalpubls.com [47] Zhang, S.; Yao, Y.; Hu, D.; Lian, W.; Qian, H.; Jie, J.; Wei, Q.; Ni, Z.; Zhang, X.; Xie, L. Application of Silicon Oxide on High Efficiency Monocrystalline Silicon PERC Solar Cells. Energies 2019, 12, 1168. [48] Xiao, X.; Zhu, H.; Liu, Z.; Tu, J. Multilayer Antireflection Coatings Design for SiO2-Passivated Silicon Solar Cells. Materialwiss. Werkstofftech. 2022, 53, 80–88. [49] Bouhafs, D.; Moussi, A.; Chikouche, A.; Ruiz, J.M. Design and Simulation of Antireflection Coating Systems for Optoelectronic Devices: Application to Silicon Solar Cells. Sol. Energy Mater. Sol. Cells 1998, 52, 79–93. [50] Xiong, C.; Xu, W.; Zhao, Y.; Xiao, J.; Zhu, X. New Design Graded Refractive Index Antireflection Coatings for Silicon Solar Cells. Mod. Phys. Lett. B 2017, 31, 1740028. [51] Ho, W.-J.; Hsu, H.-W.; Yang, H.-Y.; Liu, J.-J.; Tsai, Y.-T.; Chiu, W.-C. Plasmonic Scattering and Coupling Effects of Indium Nanoparticles Sheets Embedded in SiO2 AR-Coating on Performance Enhancement of Silicon Solar Cells. In Proceedings of the 2020 47th IEEE Photovoltaic Specialists Conference (PVSC), Virtual, 15 June–21 August 2020; pp. 0231– 0233. [52] Alone-Alaluf, M.; Appelbaum, J.; Croitoru, N. Properties of GaAs Solar Cells Coated with Diamondlike Carbon Films. Thin Solid Films 1998, 320, 159–162. [53] Liao, K.; Chen, J.; Xia, L.; Zhong, S.; Luo, X. Study about the Effect of Antireflection Coating Stacks (TiO2-SiO2/SiO2/SiNx) on the Performances of Multicrystalline Silicon Solar Cells under the Encapsulation Condition. Opt. Mater. 2020, 109, 110318. [54] Dabaghyan, G.A.; Matevosyan, L.M.; Avjyan, K.E. Determination of Refractive Index and Thickness of Nanosized Amorphous Carbon Films Via Visible Range Reflectance Spectra. J. Contemp. Phys. 2019, 54, 185–187. [55] Ma, Q.; Zhang, W.; Ma, D.; Fan, Z.; Ma, X.; Jiang, Z. Optimal Design of Quadruple-Layer Antireflection Coating Structure for Conversion Efficiency Enhancement in Crystalline Silicon Solar Cells. Optik 2019, 177, 123–130. [56] Hovhannisyan, A. Single-Layer Antireflection Coatings for GaAs Solar Cells. J. Contemp. Phys. 2008, 43, 136–138. [57] Mercy, P.A.M.; Wilson, K.S.J.; Fathima, M.I. Analysis of Reflectance of Various DLARC Systems in Solar Cells. AIP Conf. Proc. 2020, 2265, 030307. [58] Makableh, Y.F.; Vasan, R.; Sarker, J.C.; Nusir, A.I.; Seal, S.; Manasreh, M.O. Enhancement of GaAs Solar Cell Performance by Using a ZnO Sol–Gel Anti-Reflection Coating. Sol. Energy Mater. Sol. Cells 2014, 123, 178–182. [59] Khadir, A.; Kouzou, A.; Abdelhafidi, M.K. Effect of Anti-Reflective Coating on CIGS Solar Cells Performance. In Proceedings of the 2020 17th International Multi-Conference on Systems, Signals & Devices (SSD), Monastir, Tunisia, 3 July 2020; pp. 621–625. [60] Saint-Andre, S.; Rodriguez, D.; Perillo, P.; Barrera, M. TiO2 Nanotubes Antireflection Coating Design for GaAs Solar Cells. Sol. Energy Mater. Sol. Cells 2021, 230, 111201. [61] El Islam Boukortt, N.; PatanΓ©, S. High-Efficiency Cu (In1-XGax) Se2 Solar Cell Investigation with Single Layer Antireflection Coating of MgF2. In Proceedings of the 2019 2nd International Conference on Smart Grid and Renewable Energy (SGRE), Doha, Qatar, 19–21 November 2019; pp. 1–5. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 283 https://internationalpubls.com [62] Ma, C.; Zhao, C.; Fan, X.; Liu, Z.; Liu, J. Preparation of Non-Stoichiometric Al2O3 Film with Broadband Antireflective by Magnetron Sputtering. Chem. Phys. Lett. 2021, 764, 138299. [63] Bhattacharya, R.N.; Contreras, M.A.; Teeter, G. 18.5% Copper Indium Gallium Diselenide (CIGS) Device Using Single-Layer, Chemical-Bath-Deposited ZnS(O,OH). Jpn. J. Appl. Phys. Part 2 Lett. Express Lett. 2004, 43, L1475–L1476. [64] Cho, D.; Lee, W.; Kim, M.; Shin, B.; Chung, Y. Color Tuning in Cu(In,Ga)Se2 Thin-Film Solar Cells by Controlling Optical Interference in Transparent Front Layers. Prog. Photovolt. 2020, 28, 798–807. [65] Scholtz, L.; Sutta, P.; Calta, P.; Novak, P.; Solanska, M.; Mullerova, J. Investigation of Barium Titanate Thin Films as Simple Antireflection Coatings for Solar Cells. Appl. Surf. Sci. 2018, 461, 249–254. [66] WΓΌrfel, U.; Herterich, J.; List, M.; Faisst, J.; Bhuyian, M.F.M.; Schleiermacher, H.-F.; Knupfer, K.T.; Zimmermann, B. A 1 cm2 Organic Solar Cell with 15.2% Certified Efficiency: Detailed Characterization and Identification of Optimization Potential. Solar RRL 2021, 5, 2000802. [67] Suleimanov, S.; Berger, P.; Dyskin, V.; Dzhanklich, M.; Kulagina, N.; Kim, M. Increasing the Efficiency of Organic Solar Cells by Antireflection Coatings Based on Fluoride Composites. Tech. Phys. Lett. 2018, 44, 295–296. [68] Huang, X.; Sun, B.; Li, Y.; Jiang, C.; Fan, D.; Fan, J.; Forrest, S.P. 15.9% Organic Tandem Solar Cell with Extended near-Infrared Absorption. Appl. Phys. Lett. 2020, 116, 153501. [69] Kim, J.-H.; Choi, Y.J.; Lee, J.; Lee, S.G. Highly Transparent Antireflection Coatings on Fullerene-Free Organic Solar Cells Using Polymeric Nanoparticles. Thin Solid Films 2022, 742, 139043. [70] Zhang, J.; Li, B.; Song, H.; Zhao, C.; Liang, S.; Dong, Z.; Yu, J. High Refractive Index Diphenyl Sulfide Photopolymers for Solar Cell Antireflection Coatings. Energies 2022, 15, 3972. [71] Jang, W.; Park, K.H.; Wang, D.H. Increased Omnidirectional Light Absorbance by Using Hollow Silica Nanoparticles in an Anti-Reflective Pattern for Efficient Organic Photovoltaic Devices. Org. Electron. 2018, 53, 315–319. [72] Zhang, J.; Li, X.; Zhong, M.; Zhang, Z.; Jia, M.; Li, J.; Gao, X.; Chen, L.; Li, Q.; Zhang, W.; et al. Near 90% Transparent ITO-Based Flexible Electrode with Double-Sided Antireflection Layers for Highly Efficient Flexible Optoelectronic Devices. Small 2022, 18, 2201716. [73] Kim, D.I.; Lee, J.W.; Jeong, R.H.; Yang, J.W.; Park, S.; Boo, J.-H. Optical and Water- Repellent Characteristics of an Anti-Reflection Protection Layer for Perovskite Solar Cells Fabricated in Ambient Air. Energy 2020, 210, 118582. [74] Huang, K.; Yu, X.; Cong, J.; Yang, D. Progress of Graphene-Silicon Heterojunction Photovoltaic Devices. Adv. Mater. Interfaces 2018, 5, 1801520. [75] Kim, M.; Kang, T.-W.; Kim, S.H.; Jung, E.H.; Park, H.H.; Seo, J.; Lee, S.-J. Antireflective, Self-Cleaning and Protective Film by Continuous Sputtering of a Plasma Polymer on Inorganic Multilayer for Perovskite Solar Cells Application. Sol. Energy Mater. Sol. Cells 2019, 191, 55– 61. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 284 https://internationalpubls.com [76] Luo, Q.; Deng, X.; Zhang, C.; Yu, M.; Zhou, X.; Wang, Z.; Chen, X.; Huang, S. Enhancing Photovoltaic Performance of Perovskite Solar Cells with Silica Check for Nanosphere Antireflection Coatings. Sol. Energy 2018, 169, 128–135. [77] Xie, C.; Wang, Y.; Zhang, Z.-X.; Wang, D.; Luo, L.-B. Graphene/Semiconductor Hybrid Heterostructures for Optoelectronic Device Applications. Nano Today 2018, 19, 41–83. [78] Li, X.; Lv, Z.; Zhu, H. Carbon/Silicon Heterojunction Solar Cells: State of the Art and Prospects. Adv. Mater. 2015, 27, 6549–6574. [79] Shi, E.; Zhang, L.; Li, Z.; Li, P.; Shang, Y.; Jia, Y.; Wei, J.; Wang, K.; Zhu, H.; Wu, D.; et al. TiO2-Coated Carbon Nanotube-Silicon Solar Cells with Efficiency of 15%. Sci. Rep. 2012, 2, 884. [80] Bhopal, M.; Lee, D.; Rehman, M.; Seo, Y.; Lee, S. Vanadium Pentoxide (V2O5) as an Antireflection Coating for Graphene/Silicon Solar Cell. Mater. Sci. Semicond. Process. 2018, 86, 146–150. [81] Li, D.; Kunz, T.; Wolf, N.; Liebig, J.; Wittmann, S.; Ahmad, T.; Hessmann, M.; Auer, R.; Goken, M.; Brabec, C. Silicon Nitride and Intrinsic Amorphous Silicon Double Antireflection Coatings for Thin-Film Solar Cells on Foreign Substrates. Thin Solid Films 2015, 583, 25–33. [82] Shi, E.; Li, H.; Yang, L.; Zhang, L.; Li, Z.; Li, P.; Shang, Y.; Wu, S.; Li, X.; Wei, J.; et al. Colloidal Antireflection Coating Improves Graphene-Silicon Solar Cells. Nano Lett. 2013, 13, 1776–1781. [83] Sahouane, N.; Zerga, A. Optimization of Antireflection Multilayer for Industrial Crystalline Silicon Solar Cells. Energy Procedia 2014, 44, 118–125. [84] Xiao, S.; Fan, Q.; Xia, X.; Xiao, Z.; Chen, H.; Xi, W.; Chen, P.; Li, J.; Wang, Y.; Liu, H.; et al. Dependence of the Solar Cell Performance on Nanocarbon/Si Heterojunctions. Chin. Phys. B 2018, 27, 078801. [85] Yoshikawa, K.; Kawasaki, H.; Yoshida, W.; Irie, T.; Konishi, K.; Nakano, K.; Uto, T.; Adachi, D.; Kanematsu, M.; Uzu, H.; et al. Silicon Heterojunction Solar Cell with Interdigitated Back Contacts for a Photoconversion Efficiency over 26%. Nat. Energy 2017, 2, 17032. [86] Musalinov, S.; Anzulevich, A.; Bychkov, I.; Gudovskikh, A.; Shvarts, M. Influence of Double- and Triple-Layer Antireflection Coatings on the Formation of Photocurrents in Multijunction III-V Solar Cells. Semiconductors 2017, 51, 88–92. [87] Herasimenka, S.; Dauksher, W.; Boccard, M.; Bowden, S. ITO/SiOx:H Stacks for Silicon Heterojunction Solar Cells. Sol. Energy Mater. Sol. Cells 2016, 158, 98–101. [88] Park, S.; Kim, Y.; Yi, J.; Zahid, M.; Khokhar, M.; Hussain, S. Influence of Al2O3/IZO Double- Layer Antireflective Coating on the Front Side of Rear Emitter Silicon Heterojunction Solar Cell. Vacuum 2022, 200, 110967. [89] Kim, T.S.; Kim, H.J.; Geum, D.-M.; Han, J.-H.; Kim, I.S.; Hong, N.; Ryu, G.H.; Kang, J.; Choi, W.J.; Yu, K.J. Ultra-Lightweight, Flexible InGaP/GaAs Tandem Solar Cells with a Dual- Function Encapsulation Layer. ACS Appl. Mater. Interfaces 2021, 13, 13248–13253. [90] Xiao, P.; Zhang, M.; Wu, X.; Ding, K.; Pan, J.; Jie, J. Enhancing the Efficiency and Stability of Organic/Silicon Solar Cells Using Graphene Electrode and Double-Layer Anti-Reflection Coating. Sol. Energy 2022, 234, 111–118. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 285 https://internationalpubls.com [91] Kim, T.S.; Kim, H.J.; Han, J.-H.; Choi, W.J.; Yu, K.J. Flexible InGaP/GaAs Tandem Solar Cells Encapsulated with Ultrathin Thermally Grown Silicon Dioxide as a Permanent Water Barrier and an Antireflection Coating. ACS Appl. Energ. Mater. 2022, 5, 227–233. [92] Shockley, W.; Queisser, H.J. Detailed Balance Limit of Efficiency of P-n Junction Solar Cells. J. Appl. Phys. 1961, 32, 510–519. [93] El Amin, A.; Hassan, M. Fabrication Solar Cell of CdTe0.65P0.35/Si with High Efficiency Using Double-Layer Antireflection. Electr. Eng. 2018, 100, 1003–1007. [94] Campesato, R.; Greco, E.; Mezzetti, A.; di Fonzo, F.; Bissoli, F.; di Mezza, A. Effective Coating for High Efficiency Triple Junction Solar Cells. In Proceedings of the 2019 European Space Power Conference (ESPC), CΓ΄te d’Azur France, 30 September 2019; pp. 1–5. [95] Zhang, W.; Hu, K.; Tu, J.; Aierken, A.; Xu, D.; Song, G.; Sun, X.; Li, L.; Chen, K.; Zhang, D.; et al. Broadband Graded Refractive Index TiO2/Al2O3/MgF2 Multilayer Antireflection Coating for High Efficiency Multi-Junction Solar Cell. Sol. Energy 2021, 217, 271–279. [96] Singh, G.; Sekhon, J.S.; Verma, S.S. Enhanced Photocurrent in Thin-Film GaAs Solar Cells with Embedded Al Nanoparticles. Energy Sources Part A 2020, 42, 815–823. [97] Hongliang, G.; Linfeng, S.; Qiang, S.; Qiming, Z.; Yiyong, W.; Jingdong, X.; Bin, G.; Yanqing, Z. Degradation of Up-Grown Metamorphic InGaP/InGaAs/Ge Solar Cells by Low-Energy Proton Irradiation. Sol. Energy Mater. Sol. Cells 2019, 191, 399–405. [98] Chaudhry, F.; Escandell, L.; Lopez-Fraguas, E.; Vergaz, R.; Sanchez-Pena, J.; Garcia-Camara, B. Light Absorption Enhancement in Thin Film GaAs Solar Cells Using Dielectric Nanoparticles. Sci. Rep. 2022, 12, 9240. [99] Cossio, G.; Yu, E.; Tatavarti, S.; Scandrett, B.; Yu, E. Omnidirectional Current Enhancement From Laminated Moth-Eye Textured Polymer Packaging for Large-Area, Flexible III-V Solar Modules. IEEE J. Photovolt. 2021, 11, 685–691. [100] Schulze, P.; Bett, A.; Bivour, M.; Caprioglio, P.; Gerspacher, F.; Kabakl, O.; Richter, A.; Stolterfoht, M.; Zhang, Q.; Neher, D.; et al. 25.1% High-Efficiency Monolithic Perovskite Silicon Tandem Solar Cell with a High Bandgap Perovskite Absorber. Sol. RRL 2020, 4, 2000152. [101] Raj, Ashish, and Manoj Gupta. "Design and simulation of improved particle swarm optimization-based maximum power point tracking system for solar photovoltaic systems under variable illumination and partial shading conditions." In AIP Conference Proceedings, vol. 2782, no. 1. AIP Publishing, 2023. [102] Ashwini, Kumari, Ashish Raj, and Manoj Gupta. "Performance assessment and orientation optimization of 100 kWp grid connected solar PV system in Indian scenario." In 2016 International conference on recent advances and innovations in engineering (ICRAIE), pp. 1- 7. IEEE, 2016. [103] Raj, Ashish, Manoj Gupta, and Divya Suman. "Simulation of multilayer energy efficient OLEDs for flexible electronics applications." Procedia Computer Science 152 (2019): 301- 308. [104] Neethu Elizabeth Michael, Ramesh C. Bansal, Ali Ahmed Adam Ismail, A. Elnady, Shazia Hasan, A cohesive structure of Bi-directional long-short-term memory (BiLSTM) -GRU for Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 1 (2024) 286 https://internationalpubls.com predicting hourly solar radiation, Renewable Energy, Vol. 222, 2024, 119943, ISSN 0960- 1481. [105] Ahmed G. Abo-Khalil, Maaza Abdalla, Ramesh C. Bansal, Nsilulu T. Mbungu, A critical assessment of islanding detection methods of solar photovoltaic systems, Case Studies in Thermal Engineering, Vol. 52, 2023, 103681, ISSN 2214-157X, [106] Gali, Vijayakumar, B. Chitti Babu, Ramesh Babu Mutluri, Manoj Gupta, and Sunil Kumar Gupta. "Experimental investigation of Harris Hawk optimization‐based maximum power point tracking algorithm for photovoltaic system under partial shading conditions." Optimal Control Applications and Methods 44, no. 2 (2023): pp. 577-600. [107] Gali, Vijayakumar, Madisa VG Varaprasad, Sunil Kumar Gupta, and Manoj Gupta. "Performance investigation of multifunctional grid connected PV interleaved inverter with power quality enhancement." Energy Systems (2021): pp. 1-23. [108] Iqbal, Mohammad Asif, and Sunil Kumar Gupta. "TCAD based simulation and performance optimization of PPV/PCBM and Perovskite PV cells." International Journal of Computing and Digital Systems 10 (2020): 2-7. [109] Mohammad Asif Iqbal, Sunil Kumar Gupta, Comparative analysis between numerical simulation of PPV/PCBM and InGaN based solar cells, Materials Today: Proceedings, Vol. 30, Part 1, 2020, pp. 168-173, [110] Keaobaka D. Poti, Raj M. Naidoo, Nsilulu T. Mbungu, Ramesh C. Bansal, Intelligent solar photovoltaic power forecasting, Energy Reports, Vol. 9, Supplement 11, 2023, pp. 343-352, ISSN 2352-4847, [111] Sameen Maqsood, Zohaib Ali, Khuram Ali, Mubashra Ishaq, Muhammad Sajid, Ahmad Farhan, Abbas Rahdar, Sadanand Pandey, Assessment of different optimized anti-reflection coatings for ZnO/Si heterojunction solar cells,Ceramics International, Vol. 49, Issue 23, Part A, 2023, pp. 37118-37126, ISSN 0272-8842.