Tuning Optical Performance of Silicon Solar Cells with Micro-Structured Multilayer Antireflection Coatings

Abstract

This study investigates the potential of patterned multiple-layer anti-reflection coatings (MLARCs) integrated with nanocrystalline quantum dots (NQDs) to enhance silicon solar cell (Si-SC) performance by significantly reducing reflection losses. Through a combination of experimental characterization and numerical modeling, the impact of single-layer (SLARCs), continuous MLARCs, and patterned MLARCs on optical and electrical properties was assessed. The results demonstrate substantial improvements in light trapping and absorption through the implementation of patterned MLARCs.

1. Introduction

Silicon-based solar cells (Si-SCs) remain the dominant technology in the photovoltaic industry, despite their theoretical efficiency limitations imposed by the Shockley–Queisser limit. While substantial progress has been made in achieving commercial efficiencies approaching 29% under standard test conditions (STCs), significant performance losses persist due to a combination of factors, including optical reflection, thermalization, and recombination losses [1,2].

A substantial portion of incident solar radiation is reflected at the air–silicon interface owing to the mismatch in refractive indices. This reflection loss, typically around 35%, significantly reduces the overall efficiency of Si-SCs. To mitigate these losses, various anti-reflection coating (ARC) strategies, such as surface texturing, single-layer ARCs (SLARCs), and multi-layer ARCs (MLARCs), have been implemented [3,4,5,6]. However, the inefficient absorption of ultraviolet (UV) radiation by silicon, leading to approximately 10% energy loss, necessitates additional approaches to broaden the spectral response of Si-SCs [7,8,9].

Traditional ARCs, such as SiO₂ and Si₃N₄, have been widely employed to enhance light absorption and minimize reflection in Si-SCs. These materials offer compatibility with standard fabrication processes, cost-effectiveness, and proven performance across a broad spectral range. To further augment light absorption, nanocrystalline quantum dots (NQDs) have emerged as promising candidates. By downshifting high-energy photons to wavelengths more efficiently absorbed by silicon, NQDs can broaden the spectral response of Si-SCs [10,11,12]. However, the stability and durability of NQDs under environmental conditions necessitate protective measures. Lithium fluoride (LiF), with its high transparency and passivation properties, serves as an ideal encapsulation layer for NQDs, ensuring their long-term performance and stability [13,14].

Building upon these advancements, the integration of micro-/nano-patterned structures within MLARCs offers a promising avenue for further enhancing light management and device performance. By precisely controlling the dimensions and distribution of these patterns, it is possible to optimize light trapping and reduce reflection losses, leading to improved solar cell efficiency [13,14].

To address these challenges and enhance light absorption in Si-SCs, this study investigates the potential of patterned MLARCs integrated with NQDs to enhance Si-SC performance by significantly reducing reflection losses. By combining experimental characterization and numerical modeling, we aim to optimize the design and performance of these structures. The incorporation of NQDs within the MLARCs offers the potential to improve UV light absorption through downshifting while enhancing light trapping through the creation of intricate patterns. By carefully optimizing ARC design, material selection, and device configuration, this research seeks to achieve substantial improvements in the overall efficiency of silicon solar cells.

2. Proposed Device Structures

To investigate the influence of SLARCs and MLARCs on Si-SC performance, various device configurations are constructed utilizing the selected materials (SiO₂, Si₃N₄, NQDs, and LiF). The SLARC-based Si-SC comprises four distinct configurations featuring continuous thin films, as illustrated in Figure 1a. For MLARC-based Si-SCs, two primary configurations are explored: continuous and micro-/nano-patterned structures, as depicted in Figure 1b. Within the MLARC category, four specific designs are implemented: a continuous MLARC with a SiO₂/NQDs/LiF stack (b1), a continuous MLARC with a Si₃N₄/NQDs/LiF stack (b2), a patterned MLARC with a SiO₂/NQDs/LiF configuration (b3), and a patterned MLARC with a Si₃N₄/NQDs/LiF configuration (b4).

3. Experimental Procedure

This study commenced with a thorough optical characterization of SiO₂- and Si₃N₄-based SLARCs. To achieve this, a series of 18 SLARC samples were fabricated by depositing thin films of each material onto n-type (100) silicon wafers with a resistivity of less than $0.003$ ohms-cm, doped with arsenic.

SiO₂ SLARCs were produced through thermal oxidation at 1100 °C, resulting in thicknesses of 90, 120, and 150 nm (three samples for each thickness). Precise thickness measurements were obtained using a reflectometer, yielding values of $98.1\pm 0.3$ nm, $129.6\pm 0.3$ nm, and $147.0\pm 0.4$ nm, respectively. Conversely, Si₃N₄ SLARCs were fabricated via plasma-enhanced chemical vapor deposition at 770 °C and 250 mTorr, targeting thicknesses of 90, 120, and 150 nm (three samples for each thickness). The measured thicknesses for these samples were $92.5\pm 1.1$ nm, $117.6\pm 1.3$ nm, and $145.7\pm 1.5$ nm.

The optical properties of the SLARCs were determined by measuring reflectivity and refractive index using a UV-VIS spectrophotometer and ellipsometer over a spectral range of 350 to 1000 nm. To complete the optical characterization, the optical properties of NQDs and LiF films, essential components for subsequent MLARC configurations, were sourced from previous studies [13,14]. Notably, NQDs (CdSe/ZnS) were integrated into SLARCs via a mist deposition technique, while LiF was incorporated through thermal evaporation. The optical properties of the silicon substrate were referenced from Green and Keevers [15,16].

Building upon the experimentally measured optical properties of SLARCs, the second phase of the study involved integrating both SLARCs and MLARCs (SiO₂/NQDs/LiF and Si₃N₄/NQDs/LiF) into Si-SCs. To gain insight into light propagation and interaction within these complex structures, both continuous and patterned MLARC configurations were subjected to rigorous modeling and simulation using Ansys-Lumerical FDTD software.

A comprehensive analysis of the simulated structures yielded valuable optical and electrical properties, including optical reflectivity, internal and external quantum efficiencies, open-circuit voltage, short-circuit current, fill factor, and ultimately, power conversion efficiency.

4. Experimental Characterization of Si-SC Structures with SLARC

The performance of a single-layer anti-reflection coating (SLARC) is critically influenced by its refractive index (n) and thickness (d). Optimal SLARC design necessitates a refractive index that is the geometric mean of air ($n_0\approx 1$) and silicon ($n_{Si}\approx 3.5$) for the visible spectrum. Theoretically, the ideal SLARC thickness is a quarter-wavelength ($\lambda$) of the target light, as expressed below:

$$\mathbf{d}={\displaystyle \frac{\lambda }{4n}}$$

(1)

However, achieving optimal performance across the entire solar spectrum often requires deviations from this theoretical thickness. To this end, a comprehensive analysis of refractive index and optical reflectivity was conducted for SiO₂ and Si₃N₄ SLARCs with varying thicknesses across the wavelength range of 350 nm to 1000 nm. These measurements provide essential insights into the relationship between SLARC properties and their impact on solar cell performance.

4.1. Refractive Index Characteristics

The refractive index of a thin film is influenced by factors such as wavelength, temperature, and material purity. While these parameters can induce variations, standardized refractive index values are commonly employed at a reference wavelength of approximately 550 nm. Representative refractive indices at this wavelength are 3.5 for Si, 1.45 for SiO₂, 2.0 to 2.2 for Si₃N₄ (dependent on composition), 1.39 for LiF, and 1.5 to 2.5 for CdSe/ZnS NQDs (varying with quantum dot characteristics) [17,18,19].

To characterize the wavelength-dependent refractive index behavior, single-layer thin films of SiO₂, Si₃N₄, CdSe/ZnS NQDs, and LiF were deposited on n-type Si wafers. The refractive index of silicon was referenced from Green and Keevers [15,16]. For single-layer thin films, the refractive index was measured over a spectral range of 350 to 1000 nm. Figure 2 presents the measured refractive index as a function of wavelength for each single-layer thin film.

The results indicate relatively stable refractive index values for all materials across the solar spectrum (approximately 350 to 1000 nm). At a wavelength of 550 nm, the refractive indices for SiO₂, Si₃N₄, CdSe/ZnS NQDs, and LiF thin films were determined to be 1.46, 2.01, 1.67, and 1.32, respectively. Applying the quarter-wave thickness condition for optimal anti-reflection performance yielded estimated thicknesses of 101, 73, 46, and 112 nm for SiO₂, Si₃N₄, CdSe/ZnS NQDs, and LiF thin films, respectively. These calculated thicknesses served as a foundation for the design of both continuous and patterned MLARC and SLARC structures, specifically SiO₂/NQD/LiF and Si₃N₄/NQD/LiF configurations.

4.2. Optical Reflectivity Characteristics

Theoretically, the Fresnel equations describe the reflection and transmission of light when it encounters an interface between two different media. For normal incidence, the reflectivity $\mathbf{R}$ at an interface between two materials with refractive indices $n_1$ and $n_2$ is given by:

$$\mathbf{R}={\left({\displaystyle \frac{n_1-n_2}{n_1+n_2}}\right)}^2$$

(2)

When a thin film of refractive index $n_2$ and thickness d is applied to a substrate with refractive index n₃, and the incident medium is air ($n_1$ ≈ 1), the total reflectivity ${\mathbf{R}}_{total}$ is influenced by interference effects. The reflectivity can be calculated using the following formula, which considers the constructive and destructive interference of light reflected from the top and bottom surfaces of the thin film:

$${\mathbf{R}}_{total}={\left|{\displaystyle \frac{r_{12}+r_{23}{e}^{2i\delta }}{1+r_{12}{r}_{23}{e}^{2i\delta }}}\right|}^2$$

(3)

where $r_{12}$ is the reflection coefficient at the air–film interface, $r_{23}$ is the reflection coefficient at the film–substrate interface, and $\delta$ is the phase difference due to the path length in the film. These parameters can be calculated as follows:

$${\mathbf{r}}_{12}=\left({\displaystyle \frac{n_1-n_2}{n_1+n_2}}\right){\mathbf{r}}_{23}=\left({\displaystyle \frac{n_2-n_3}{n_2+n_3}}\right)\delta ={\displaystyle \frac{2\pi n_{2}d}{\lambda }}$$

(4)

The optical reflectivity of n-type silicon substrates was systematically investigated, both in bare form and with the application of SiO₂ or Si₃N₄ SLARCs. A series of samples were prepared, incorporating SLARC thicknesses of 90 nm, 100 nm, and 150 nm. Figure 3 presents the spectral reflectivity of these structures across a wavelength range of 350 nm to 1000 nm, with comparative data for intrinsic silicon included as a reference point [15,16].

Figure 3 presents a comparative analysis of reflectivity spectra for various n-type silicon substrates both with and without the application of SLARCs within the wavelength range of 350 nm to 1000 nm. The baseline reflectivity of n-type Si is established in Figure 3a, revealing comparable reflection characteristics to the reference intrinsic silicon spectrum. The introduction of SiO₂ and Si₃N₄ SLARCs significantly reduces reflectivity, particularly within the visible spectrum, as evident in Figure 3b,c, with varying thicknesses. A correlation between SLARC thickness and reflectivity is observed, although interference effects can occur at greater thicknesses. However, The correlation between thickness and reflectivity exhibits variability across different wavelengths. While the refractive index remains relatively constant within the measured wavelength range, the relationship between SLARC thickness and reflectivity is not straightforward. Other factors, such as interference effects and material properties, likely influence the observed behavior. Figure 3d contrasts the reflectivity of SiO₂ and Si₃N₄ SLARCs (both 90 nm-thick) with that of n-type Si, and highlights the superior anti-reflective properties of Si₃N₄ compared to SiO₂ across a broader wavelength range. Notably, the Si₃N₄ SLARC with a thickness of 90 nm exhibits a minimum reflectivity of 0.16% at 750 nm compared to 9% for SiO₂ counterpart at 650 nm.

The optimal spectral region for Si-SC light absorption spans from 350 nm to 1000 nm, with peak absorption efficiency typically occurring between 450 nm and 750 nm, centered around 600 nm.

Table 1. Measured reflectivity of n-type Si substrates with and without SLARCs at different thicknesses and wavelengths, against reflectivity of intrinsic Si (reference data from Green and Keevers [15]).

Structure	Thickness (nm)	Wavelength (nm)
		350	450	550	650	750
Si (no ARC)	intrinsic	56.45	41.96	36.73	34.73	33.24
Si (no ARC)	n-type	68.98	44.18	37.63	34.93	33.43
Si with SiO2 SLARC	90	68.95	24.67	10.85	9.15	11.24
	120	66.15	40.70	22.10	11.34	7.64
	150	50.97	44.23	30.02	17.37	9.88
Si with Si3N4 SLARC	90	60.20	39.76	16.77	3.64	0.16
	120	7.62	42.11	34.35	20.15	8.36
	150	65.46	12.92	35.30	33.31	24.17

provides a quantitative comparison of reflectivity values for n-type Si with and without SLARCs at key wavelengths within this range, alongside reference data for intrinsic Si. Both intrinsic and n-type Si exhibit relatively high reflectivity across the measured spectrum, with a decreasing trend towards longer wavelengths. The introduction of SiO₂ and Si₃N₄ SLARCs significantly reduces reflectivity, particularly in the visible range (450 nm to 750 nm). SLARC thickness affects reflectivity, with thinner SiO₂ SLARCs generally showing lower reflectivity. However, this trend is less pronounced for Si₃N₄ SLARCs. Reflectivity varies significantly with wavelength and SLARC thickness, highlighting the importance of considering the entire solar spectrum for SLARC and MLARC optimization. These experimental results serve as a foundation for subsequent modeling and simulation studies of Si-SC structures incorporating SLARCs and MLARCs.

5. Modeling and Simulating Si-SC Structures

To optimize Si-SC performance, a comprehensive modeling and simulation framework was employed. As illustrated in Figure 4, the optimization workflow of a two-step modeling approach was adopted. Initially, the optical properties of constituent materials (SiO₂, Si₃N₄, LiF, and CdSe/ZnS NQDs) were experimentally determined, providing a foundation for subsequent simulations. These optical parameters, including refractive index and extinction coefficient, were incorporated into the Ansys−Lumerical−FDTD simulation environment.

Utilizing the FDTD method, the optical performance of various SLARC and MLARC configurations was meticulously analyzed. By systematically varying layer thicknesses, materials, and structural parameters, a comprehensive design space was explored. Key optical metrics, such as absorption, reflection, and transmission spectra, were assessed to identify optimal ARC designs that maximized light harvesting within the Si-SC.

To evaluate the electrical implications of the optimized ARC designs, the Lumerical CHARGE platform was integrated. Coupling optical generation data from FDTD simulations with device-level electrical models enabled a comprehensive assessment of Si-SC performance. Key electrical parameters, including short-circuit current, open-circuit voltage, and fill factor, were determined. Iterative optimization of ARC structures was conducted to achieve a balance between optical and electrical performance, ultimately enhancing overall Si-SC power conversion efficiency.

5.1. Optical Modeling and Simulation

A detailed understanding of light interaction with the Si-SC is essential for optimizing ARC design. The FDTD method was employed to compute the optical absorption spectrum across the relevant wavelength range (350 nm to 1100 nm). By considering the electric field intensity $\left|E\right|$ and material permittivity $img\left(\epsilon \right)$, the absorbed power ($\mathit{Pabs}$) was calculated using Equation (5).

$$\mathbf{Pabs}=-0.5\omega \times {\left|E\right|}^2\times img\left(\epsilon \right)$$

(5)

Quantum efficiency (QE), defined as the ratio of $Pabs$ to incident power ($P_{in}$), was determined for each wavelength using Equation (6).

$$\mathbf{QE}\left(\lambda \right)={\displaystyle \frac{Pabs\left(\lambda \right)}{P_{in}\left(\lambda \right)}}$$

(6)

To provide spatial resolution of efficiency, local quantum efficiency (QE_local) was calculated, considering optical transmission and absorption at specific locations within the device:

$${\mathbf{QE}}_{local}(x,y,z)=\mathrm{QE}\left(\lambda \right)\times {\mathrm{T}}_{opt}(x,y,z,\lambda )\times {\mathrm{A}}_{opt}(x,y,z,\lambda )$$

(7)

The optical generation rate per unit volume, denoted as ${\mathit{G}}_v\left(\lambda \right)$, representing the rate at which electron–hole pairs are generated within a material per unit volume in response to incident photons at a specific wavelength $\lambda$, was calculated using:

$${\mathbf{G}}_v\left(\lambda \right)={\mathrm{A}}_{opt}\left(\lambda \right)\times {\mathrm{I}}_{ph}\left(\lambda \right)$$

(8)

where ${\mathit{I}}_{ph}$ represents the incident photon flux at wavelength $\lambda$.

5.2. Electrical Modeling and Simulation

The electrical performance of the optimized ARC designs was assessed using the Lumerical CHARGE platform. By coupling optical generation data with device-level models, the short-circuit current density (J_sc) was calculated using Equation (9), considering the spatial distribution of carrier generation and local quantum efficiency.

$${\mathbf{J}}_{sc}={\int }_{\omega }q\times {\mathrm{G}}_v(x,y,z)\times {\mathrm{QE}}_{local}(x,y,z)dxdydz$$

(9)

where $\mathit{q}$ is elementary charge.

The open-circuit voltage (V_oc) was estimated using Equation (10), incorporating Boltzmann statistics and the reverse saturation current density.

$${\mathbf{V}}_{oc}={\displaystyle \frac{kT}{q}}ln({\displaystyle \frac{J_{sc}}{J_o}}+1)$$

(10)

where k is the Boltzmann constant, T is the absolute temperature in Kelvin and J_o is the reverse saturation current density.

Finally, the power conversion efficiency (PCE) was determined using Equation (11), considering the fill factor (FF) calculated from the maximum power point.

$$\mathbf{PCE}={\displaystyle \frac{J_{sc}{V}_{oc}FF}{P_{in1.5G}}}\times 100.$$

(11)

To comprehensively assess solar cell performance, both internal quantum efficiency (IQE) and external quantum efficiency (EQE) are essential metrics. EQE is determined by the interplay between optical efficiency (OE) and IQE. OE represents the fraction of incident light that is absorbed by the device, while IQE characterizes the efficiency of converting absorbed photons into collected charge carriers. Mathematically, EQE can be expressed as:

$$EQE\left(\lambda \right)=OE\left(\lambda \right)\times IQE\left(\lambda \right)$$

(12)

where OE is calculated as:

$$OE=1-R-T$$

(13)

with R and T representing the total reflected and transmitted power, respectively.

To accurately capture the optical and electrical behavior of Si-SCs, the FDTD simulations employed a refined mesh with a plane wave incident source covering the wavelength range of 350 nm to 1100 nm. Solar generation calculations were incorporated within the silicon layer to determine the spatial distribution of carrier generation. This comprehensive modeling approach provides a robust foundation for understanding the interplay between ARC design, optical properties, and electrical performance in Si-SCs.

5.3. Modeling and Simulation of Si-SC with SLARC

The optical reflectivity of Si-SC structures with and without SLARCs was experimentally and numerically investigated. SLARCs composed of SiO₂ and Si₃N₄, each with a thickness of 90 nm, were fabricated and characterized. Figure 5 presents the measured and simulated reflectivity spectra for these structures. A comparative analysis of reflectivity values at specific wavelengths is provided in

Table 2. Measured and simulated reflectivity of Si-SC structures with and without SLARC of SiO₂ (90 nm) and Si₃N₄ (90 nm).

Structure	Type	Wavelength (nm)
		350	450	550	650	750
Si-SC (no ARC)	measured	68.98	44.18	37.63	34.93	33.43
	simulated	51.98	45.77	41.50	38.45	35.86
Si-SC with SiO2 SLARC	measured	68.95	24.67	10.85	9.15	11.24
	simulated	46.62	22.52	13.52	13.85	16.27
Si-SC with Si3N4 SLARC	measured	60.20	39.76	16.77	3.64	0.16
	simulated	47.54	41.61	16.98	2.58	0.23

. A strong correlation was observed between the experimental and simulated reflectivity data for Si-SC structures with and without SLARCs, validating the accuracy of the modeling approach.

The obtained reflectivity data, in conjunction with refractive index measurements, enabled the calculation of optimal SLARC thicknesses based on the quarter-wave principle at a reference wavelength of 550 nm. The resulting SLARC configurations (SiO₂: 101 nm, Si₃N₄: 73 nm) were then simulated to assess their impact on reflectivity across the solar spectrum (Figure 5b).

To evaluate the electrical performance of the optimized SLARC structures, the IQE and EQE of Si-SCs were determined. The device structure was modeled using a top SiO₂ or Si₃N₄ layer, a silver back reflector, and an aluminum emitter. Surface recombination velocities were assigned as follows: 1000 cm/s for aluminum, 10⁷ cm/s for silver, and 1000 cm/s for both electrons and holes at the SiO₂-Si and Si₃N₄-Si interfaces. In the electrical simulation, the electron and hole concentrations in the Si-SC are both set to 1 × 10²⁰ cm⁻³ [20].

Table 3. IQE and EQE of Si-SC structures with and without SLARCs of SiO₂ (101 nm) and Si₃N₄ (73 nm), at selected wavelengths: 350, 550, and 750 nm.

	IQE $(\%)$			EQE $(\%)$
Structure	350	550	750	350	550	750
Si-SC (no ARC)	90.54	96.71	99.36	43.46	56.57	63.49
Si-SC with SiO2 SLARC	95.93	96.69	99.47	46.65	82.19	87.13
Si-SC with Si3N4 SLARC	90.55	96.60	99.25	41.81	93.14	94.05

presents a comparative analysis of IQE and EQE at selected wavelengths for Si-SCs with and without SLARC of SiO₂ (101 nm) and Si₃N₄ (73 nm). While IQE provides insights into intrinsic material properties, EQE reflects the overall device efficiency, including optical losses. The observed discrepancies between IQE and EQE at shorter wavelengths highlight the impact of surface recombination on charge carrier collection.

The electrical characteristics of Si-SCs, including $V_{oc}$, $J_{sc}$, FF, and PCE, were determined using Lumerical CHARGE simulator. The calculated J-V curves (Figure 6) reveal the impact of SLARCs on device performance. The observed enhancement in $J_{sc}$ for SLARC-coated devices is attributed to the improved light harvesting efficiency, as evidenced by the reduced reflectivity.

Table 4. Electrical characteristics of Si-SC structures with and without SLARCs of SiO₂ (101 nm) and Si₃N₄ (73 nm).

Structure	${\mathit{V}}_{\mathit{oc}}$ ($\mathbf{V}$)	${\mathit{J}}_{\mathit{sc}}$ (mA/cm2)	FF	PCE (%)
Si-SC (no ARC)	$0.59$	$25.18$	$0.82$	$12.27$
Si-SC with SiO2 SLARC	$0.60$	$33.67$	$0.82$	$16.68$
Si-SC with Si3N4 SLARC	$0.60$	$37.11$	$0.82$	$18.47$

summarizes the key electrical performance parameters for Si-SC structures with and without SLARCs. The inclusion of SiO₂ and Si₃N₄ SLARCs resulted in significant enhancements in $J_{sc}$ from 25.18 mA/cm² to 37.11 mA/cm², correspondingly increasing PCE from 12.27% to 18.47%. While $V_{oc}$ and FF remained relatively constant, the observed improvements in $J_{sc}$ and PCE directly correlate with the enhanced light harvesting capabilities of Si-SC with SLARCs, as evidenced by the IQE and EQE data.

5.4. Modeling and Simulation of Si-SC with Continuous MLARC

The optical performance of continuous MLARC configurations comprising SiO₂/NQD/ LiF and Si₃N₄/NQD/LiF was investigated using Lumerical FDTD simulations. The boundary conditions of the solver are set as periodic in the x and y directions to enable light propagation along the z-axis. Optimal layer thicknesses were determined through parametric studies, resulting in configurations of 40 nm SiO₂, 40 nm NQD, and 100 nm LiF for the first structure, and 110 nm Si₃N₄, 50 nm NQD, and 70 nm LiF for the second.

Figure 7a compares the reflectivity of these MLARCs with the reference Si-SC structure. The SiO₂/NQD/LiF MLARC demonstrated a significant reduction in reflectivity, particularly in the longer-wavelength region. While the Si₃N₄/NQD/LiF MLARC exhibited lower reflectivity across the entire spectrum, it showed a more pronounced reduction in the visible range. The implementation of continuous MLARC configurations yielded a substantial reduction in overall optical reflectivity compared to SLARC structures, underscoring the enhanced light-trapping capabilities of the multi-layer design.

To assess the impact of these MLARC configurations on Si-SC performance, IQE and EQE were calculated.

Table 5. IQE and EQE of Si-SC structures with and without continuous MLARCs of SiO₂/NQD/LiF and Si₃N₄/NQD/LiF configurations, at selected wavelengths: 350, 550, and 750 nm.

	IQE $(\%)$			EQE $(\%)$
Structure	350	550	750	350	550	750
Si-SC (no ARC)	90.54	96.71	99.36	43.46	56.57	63.49
Si-SC with SiO2/NQD/LiF C-MLARC	96.49	98.12	99.59	63.09	72.73	86.96
Si-SC with Si3N4/NQD/LiF C-MLARC	96.48	98.34	99.51	81.16	83.93	82.07

presents a comparative analysis of these parameters. Both MLARC configurations exhibited improved EQE compared to the SLARC structures, particularly at shorter wavelengths, attributed to the enhanced light harvesting capabilities of the NQD layer, facilitated by its downshifting effect. However, the Si₃N₄/NQD/LiF configuration showed a decrease in EQE at longer wavelengths, due to the change in the reflectivity.

The electrical performance of Si-SCs with continuous MLARCs was evaluated through J-V characteristic simulations, as shown in Figure 7b. In addition,

Table 6. Electrical characteristics for Si-SC structures with and without continuous MLARC of SiO₂/NQD/LiF and Si₃N₄/NQD/LiF configurations.

Structure	${\mathit{V}}_{\mathit{oc}}$ ( $\mathbf{V}$)	${\mathit{J}}_{\mathit{sc}}$ (mA/cm2)	FF	PCE (%)
Si-SC (no ARC)	$0.59$	$25.18$	$0.82$	$12.27$
Si-SC with SiO2/NQD/LiF C-MLARC	$0.61$	$34.10$	$0.83$	$17.26$
Si-SC with Si3N4/NQD/LiF C-MLARC	$0.61$	$35.54$	$0.83$	$18.02$

summarizes the key electrical performance parameters for Si-SC structures with and without MLARCs. The calculated $J_{sc}$ values for the SiO₂/NQD/LiF and Si₃N₄/NQD/LiF configurations were 34.1 mA/cm² and 35.54 mA/cm², respectively, representing improvements over the SLARC-based Si-SCs. Corresponding PCE values of 17.26% and 18.02% were obtained.

5.5. Modeling and Simulation of Si-SC with Patterned MLARC

To investigate the potential of patterned MLARCs, the SiO₂/NQD/LiF and Si₃N₄/NQD/LiF configurations were simulated using Lumerical FDTD. As shown in Figure 8, the geometric parameters, including layer thicknesses (d), period (P), and radius (L) of the cylindrical patterns, were optimized. The Lumerical FDTD simulation tool was employed to simulate these structures, with periodic boundary conditions applied in the x and y directions to mimic an infinite array of patterns, while light propagation was modeled along the z-axis.

The optimization of patterned MLARCs involved a systematic variation of the period (P) of the cylindrical patterns, while maintaining a constant L/P ratio of approximately $0.32$. This approach allowed for an assessment of the impact of pattern periodicity on the overall device performance. By simulating Si-SC structures with varying P values within the range of $250 \mathrm{n}\mathrm{m}$ to $600 \mathrm{n}\mathrm{m}$, the sensitivity of $J_{sc}$ to the pattern period was investigated. As depicted in Figure 8, $J_{sc}$ initially increases with increasing P, reaching a maximum value at an optimal period before decreasing at larger P values. This behavior indicates the existence of an optimal pattern periodicity that maximizes light trapping and carrier generation.

The observed trend can be attributed to the interplay between light scattering, diffraction, and interference effects within the patterned structure. At smaller periods, light scattering is less efficient, leading to reduced light trapping. Conversely, at larger periods, excessive light scattering can occur, resulting in increased reflection losses. The optimal period represents a balance between these competing effects, maximizing light absorption and minimizing reflection. By conducting a parametric study across a range of d, P, and L values, through rigorous optimization, the following d values were determined: 80 nm SiO₂, 40 nm NQD, and 60 nm LiF for the SiO₂/NQD/LiF configuration; 60 nm Si₃N₄, 60 nm NQD, and 60 nm LiF for the Si₃N₄/NQD/LiF configuration. The cylindrical patterns of NQD and LiF layers were optimized with (P) of 550 nm and (L) of 175 nm. The optimization analysis identified the optimal geometric parameters of the pattern for each MLARC configuration, providing valuable insights for the design of high-performance Si-SCs.

Figure 9a presents the reflectivity spectra of the patterned MLARC configurations. Both structures exhibited significantly reduced reflectivity compared to their continuous counterparts, particularly in the visible and near-infrared regions. The Si₃N₄/NQD/LiF configuration demonstrated superior light trapping capabilities, achieving a minimum reflectivity of 5% at 550 nm.

The impact of patterned MLARCs on carrier generation was assessed through IQE and EQE calculations.

Table 7. IQE and EQE of Si-SC structures with patterned MLARCs of SiO₂/NQD/LiF and Si₃N₄/NQD/LiF configurations.

	IQE (%)			EQE (%)
Structure	350	550	750	350	550	750
Si-SC (no ARC)	90.54	96.71	99.36	43.46	56.57	63.49
Si-SC with SiO2/NQD/LiF P-MLARC	96.47	98.12	99.50	58.39	86.35	87.27
Si-SC with Si3N4/NQD/LiF P-MLARC	95.95	97.80	99.41	64.62	94.96	95.08

presents the results, indicating a substantial enhancement in EQE for both configurations compared to the SLARC and continuous MLARC counterparts. This improvement is attributed to the combined effects of light trapping of the optimized cylindrical patterns and downshifting within the NQD layer.

To evaluate the electrical performance of patterned MLARCs, J-V characteristics were simulated, as shown in Figure 9b. In addition,

Table 8. Electrical characteristics for Si-SC structures with patterned MLARC of SiO₂/NQD/LiF and Si₃N₄/NQD/LiF configurations.

Structure	${\mathit{V}}_{\mathit{oc}}$ ($\mathbf{V}$)	${\mathit{J}}_{\mathit{sc}}$ (mA/cm2)	FF	PCE (%)
Si-SC (no ARC)	$0.59$	$25.18$	$0.82$	$12.27$
Si-SC with SiO2/NQD/LiF P-MLARC	$0.61$	$39.52$	$0.83$	$20.13$
Si-SC with Si3N4/NQD/LiF P-MLARC	$0.62$	$48.04$	$0.83$	$24.65$

summarizes the key electrical performance parameters for Si-SC structures with and without patterned MLARCs. The calculated $J_{sc}$ values for the SiO₂/NQD/LiF and Si₃N₄/NQD/LiF patterned MLARCs were 39.51 mA/cm² and 48.04 mA/cm², respectively, representing significant improvements over the continuous MLARC and SLARC configurations. The corresponding PCE values were 20.12% and 24.65%.

Overall, the optimized patterned MLARC structures exhibited reduced reflectivity compared to their continuous counterparts, with the Si₃N₄/NQD/LiF configuration demonstrating superior performance. The introduction of periodic patterns led to enhanced light trapping and improved absorption, as evidenced by the increased IQE and EQE values. These findings were further corroborated by the electrical performance analysis, which revealed significant improvements in $J_{sc}$ and PCE for the patterned MLARC structures.

By correlating microscopic optical properties with macroscopic device performance,

Table 9. Optical and electrical characteristics for Si-SC structures with no ARC, SLARC, continuous (C-MLARC) and patterned (P-MLARC) of SiO₂/NQD/LiF and Si₃N₄/NQD/LiF configurations.

Structure	Optical Parameters						Electrical Parameters
	350 (nm)		550 (nm)		750 (nm)		-
	R (%)	EQE (%)	R (%)	EQE (%)	R (%)	EQE (%)	J (mA/cm2)	PCE (%)
Si-SC (no ARC)	51.98	43.46	41.50	56.57	35.86	63.49	25.18	12.27
Si-SC (SiO2 SLARC)	51.85	46.65	14.99	82.19	12.39	87.13	33.67	16.68
Si-SC (SiO2 C-MLARC)	34.62	63.09	25.68	72.73	12.68	86.96	34.10	17.26
Si-SC (SiO2 P-MLARC)	39.47	58.39	11.99	86.35	12.16	87.27	39.52	20.13
Si-SC (Si3N4 SLARC)	53.83	41.81	3.58	93.14	5.01	94.05	37.11	18.47
Si-SC (Si3N4 C-MLARC)	15.89	81.16	14.65	83.94	17.52	82.07	35.54	18.02
Si-SC (Si3N4 P-MLARC)	32.64	64.62	2.91	94.96	4.35	95.08	48.04	24.65

presents a comparative overview of reflectivity, EQE, $J_{sc}$, and PCE for different Si-SC structures. The results underscore the significant impact of ARC design on light absorption and charge carrier generation to optimize light management and enhance Si-SC performance. The enhanced performance of Si-SC with patterned MLARCs can be attributed to several factors:

• Improved light trapping: The periodic patterns scatter incident light, increasing the optical path length within the active region and promoting multiple reflections, leading to enhanced light absorption.
• Enhanced carrier generation: The NQD layer absorbs photons at shorter wavelengths and re-emits them at longer wavelengths through a downshifting process. These downshifted photons are more effectively absorbed by the semiconductor layer, resulting in increased carrier generation.
• Reduced reflection losses: The optimized pattern design minimizes reflection at the top surface of the solar cell, allowing a higher proportion of incident light to be coupled into the device.

These combined effects contribute to the significant improvements in Jsc, EQE, and overall PCE observed for the patterned MLARC configurations.

6. Conclusions

This study underscores the pivotal role of ARCs in enhancing Si-SC efficiency. By systematically investigating SLARCs, continuous MLARCs, and patterned MLARCs, we have demonstrated the effectiveness of these approaches in mitigating reflection losses and optimizing light absorption. The incorporation of NQDs within micro-/nano-patterned MLARCs further amplified light trapping and absorption, leading to substantial improvements in device performance. By combining experimental characterization and numerical modeling, this research demonstrated that the optimized patterned MLARC configuration achieved a 45% reduction in reflectivity relative to the reference Si-SC, ultimately contributing to overall performance gains.

The results presented herein highlight the potential of advanced ARC technologies to significantly enhance Si-SC efficiency. While this study has focused on optical and electrical performance, future research should explore the integration of these optimized ARC designs with strategies to address electrical and thermal losses. By combining these advancements, the realization of high-efficiency, cost-effective silicon-based solar cells can be accelerated.