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. 2025 Aug 22;20(1):144. doi: 10.1186/s11671-025-04329-0

Hybrid Ag nanocone–Al2O3/Si nanopillar periodic array for broadband anti-reflection

Xiangyao Luo 1, Wen Sun 1, Zichen Xiong 1, Yue Chang 1, Wenyi Ren 1, Xinyu An 2, He Wang 1, Hongchang An 1,✉
PMCID: PMC12373969  PMID: 40844676

Abstract

In this paper, a periodic array of Ag nanocones and Al2O3/Si nanopillars (AgNCs–Al2O3/SiNPs) deposited on a semiconductor substrate is designed, and their anti-reflection property is investigated systematically using the finite difference time domain method (FDTD). The obtained results show that the designed structure achieves a weighted reflectance as low as 1.99% over a broad spectral range of 400–1100 nm. The anti-reflection mechanism of the AgNC–Al2O3/SiNP array is elucidated through calculations of the scattering cross-section and electric field distribution of the AgNC array. The localized surface plasmon resonance (LSPR) effects of AgNC array, together with the multiple scattering and reflection effects of the SiNP array, can reduce the reflectance to some extent. Furthermore, the introduction of Al2O3 spacer layer leads to an additional decrease in reflectivity. In addition, the reflective properties of three alternative metal nanocones (Al, Cu, and Au), combined with the Al2O3/SiNP array on a Si substrate, are evaluated. Among these composite structures, the CuNC–Al2O3/SiNP array exhibits the lowest reflectivity of 1.66%. This study enriches the localized surface plasmon model and provides a theoretical foundation for the design of plasmonic solar cells and other optoelectronic devices requiring low reflectivity.

Keywords: Anti-reflection technique, Localized surface plasmon, Nanopillar, Silicon solar cells

Introduction

Minimizing unwanted light reflection on the surface of solar cells is crucial for improving their efficiency [1]. Traditional anti-reflection coating (ARC) technologies [2–4] are based on the destructive interference of reflected light at different interfaces. This quarter-wavelength approach is effective in reducing reflection for incident light at specific wavelengths and angles. To achieve broadband and wide-angle anti-reflection, however, multilayer coatings [5] are usually required, which is unfavorable for reducing the cost of solar cells. Micro-texturing techniques, such as pyramid [5, 6] or inverted pyramid [7, 8] features, reduce surface reflection through multiple internal reflections. These internal reflections extend the optical path length within the active layer, thereby enhancing the probability of light absorption. Such methods are suitable for monocrystalline silicon solar cells, where the optically thick substrate can provide a sufficiently long optical path length to ensure effective absorption. However, in thin-film solar cells, light trapping performance is limited because light can escape the active layer before being fully absorbed. To reduce silicon usage and further lower the cost of solar cells, nano-texturing and plasmonic light trapping technologies have been developed to suppress surface reflection and enhance light absorption.

Nano-texturing techniques [9–17], based on the effective refractive index theory and Mie scattering, have been widely explored for anti-reflection applications. Various Si nanostructures, such as nanowires, nanopillars, and nanocones, have been extensively studied in recent years. These studies demonstrate that sufficiently long Si nanostructures are required to achieve excellent anti-reflective performance, but excessively long structures may compromise mechanical stability. Therefore, reducing the height of Si nanostructures while maintaining low reflectance remains a critical research objective. Another effective anti-reflection strategy is plasmonic light trapping [18–26], which employs plasmonic nanostructures—typically composed of noble metals such as Au or Ag—to enhance light absorption via localized surface plasmon effects, including near-field electromagnetic enhancement and far-field scattering. This technique is particularly advantageous for thin-film solar cells, as it scatters incident light laterally or at oblique angles, thereby increasing the optical path length within the active layer without requiring a thick substrate. However, the LSPR peaks of metallic nanoparticles are generally narrow in spectral width [21], necessitating careful structural design to achieve broadband optical response. To address this limitation, a hybrid approach that integrates nano-texturing and plasmonic light trapping has been proposed to suppress surface reflectance. Huang et al. [27] investigated the anti-reflection properties of composite structures composed of Ag nanospheres and Si nanopillars on a Si substrate. Similarly, Sharuma et al. [28] replaced Ag nanospheres with Al, Cu, and Au nanospheres to compare their respective reflectance behaviors. Beyond nanosphere geometry, nanocone [17, 23, 24, 29–31], another representative regular structure, exhibits strong localized energy concentration at regions of high curvature, particularly at the apex and along the base edge. This geometric characteristic leads to pronounced near-field enhancement under LSPR excitation, a phenomenon known as the “Tip Effect” [29, 32–34], which significantly enhances light scattering efficiency [30]. Owing to these unique optical properties, the tip effect holds great promise for applications in sensoring [35], imaging [36], field emission [37], and surface-enhanced Raman scattering [38]. To our knowledge, a periodic array of metallic nanocones and SiNPs has not been investigated for anti-reflection enhancement. Moreover, the dielectric spacer layer plays a critical role in modulating the forward scattering of the AgNC array. Based on these insights, we design and systematically analyze a periodic AgNC–Al2O3/SiNP array to achieve superior anti-reflective performance.

The structure of this study is organized as follows: Sect. 2 introduces the proposed model and research methodology. Section 3 provides a detailed investigation of the anti-reflection properties of various configurations, including the SiNP array, Al2O3/SiNP array, AgNC array, AgNC–SiNP array, and AgNC–Al2O3/SiNP array. In addition to reflectance, the scattering cross-section and electric field distribution of the AgNC are analyzed to elucidate the underlying mechanisms contributing to the low reflectance of the proposed model. Furthermore, as an extension of AgNC, the reflective characteristics of three alternative metal nanocones (Al, Cu, Au) integrated with the Al2O3/SiNP array are also examined. Finally, Sect. 4 presents the conclusions.

Design and methodology

The designed model is a two-dimensional periodic array of AgNCs–Al2O3/SiNPs deposited on a Si substrate, as illustrated in Fig. 1. Five geometric parameters shown in Fig. 1a are included: the period (P) of the square array, the height (H1) of the SiNP, the height (H2) of Al2O3 layer, the radius (R) of nanopillar, and the equivalent spherical radius (Inline graphic) of the Ag nanoparticle. The equivalent spherical radius refers to the radius of a sphere having the same volume as a nonspherical object, calculated as Inline graphic, where V is the geometric volume of the object. To simulate the interaction of incident light with the model, the software Ansys Lumerical FDTD (2014R2) is employed. The simulation box has dimensions of 0.4 × 0.4 × 1 μm3. Perfectly matched layer (PML) boundary conditions are applied to the top and bottom boundaries of the box and periodic boundary conditions (PBC) are used for the remaining four faces. Optical constants for Si, Al, Cu, Ag, Au, and Al2O3 are taken from Palik [39]. A Total-Field Scattered-Field (TFSF) source is used to introduce a normally incident broadband plane wave (400–1100 nm) from the top of the simulation box along the z-axis. A non-uniform mesh is used in the simulation region, with a minimum mesh size of 2 nm for the AgNC array. The nanocone is characterized by a height equal in magnitude to its base diameter, and its central axis is aligned with those of both the SiNP and the Al2O3 NP within each unit cell shown in Fig. 1b throughout this study. Reflectance is defined as the ratio of reflected intensity to incident intensity. The scattering cross-section [40] is defined as the ratio of the time-averaged power scattered by an obstacle to the power density of the incident wave.

Fig. 1.

Fig. 1

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a Schematic illustration of the proposed model and b cross-sectional view of the unit cell at x = 0

The solar spectrum weighted reflectance (SWR) [41] is an indicator used to evaluate the reflectance characteristics of a material over the entire solar spectrum. It provides a comprehensive reflectance value by performing a weighted average of the reflectance at different wavelengths, based on the spectral energy distribution of sunlight. The SWR in the wavelength range from λ1 to λ2 is calculated using the following formula:

graphic file with name d33e442.gif 1

where λ is the wavelength of incident light, λ1 and λ2 are the lower and upper bounds of the wavelength range, respectively. R(λ) is the reflectance of the structure at wavelength λ, and I(λ) is the spectral irradiance of the solar spectrum at wavelength λ, which is obtained from the website [42].

Results and discussion

The wavelength-dependent reflectance spectra of a SiNP array (red) and an Al2O3/SiNP array (green), both fabricated on a Si substrate, are shown in Fig. 2. The reflectance of the bare flat Si surface (black) serves as a reference. It is well known that when light is normally incident from air onto a flat Si surface, the significant mismatch in refractive index leads to more than 30% reflection [1]. By introducing a textured SiNP array, the average reflectance is significantly reduced compared to that of bare flat Si substrate. After optimization, the geometric parameters of the SiNP array are determined to be R = 175 nm, H1 = 100 nm, H2 = 70 nm, and P = 400 nm, yielding a reflectance of 10.96% and a SWR of 10.16%. These results are in good agreement with those reported in previous studies [27, 28]. The effectiveness of the SiNP array in suppressing surface reflection is primarily attributed to two mechanisms. First, incident light undergoes multiple refraction and scattering events among the vertically aligned nanopillars, effectively extending the optical path length and thereby increasing the probability of photon absorption within the structure, which results in reduced reflection [12]. Second, the Si nanopillars, together with the air gaps between them, form an effective medium with a graded refractive index that transitions smoothly from that of air to Si substrate. This gradual refractive index profile alleviates the abrupt mismatch at the interface, thereby suppressing reflection [10].

Fig. 2.

Fig. 2

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Reflectivity spectra of the SiNP array (red) and Al2O3/SiNP array (green) on a Si substrate, with the bare flat Si surface (black) as a reference

In addition, Al2O3 is widely employed for surface passivation of semiconductor materials in solar cells due to its ability to effectively reduce surface defect states, thereby decreasing the surface recombination rate of charge carriers. This passivation effect is vital for improving photovoltaic performance and enhancing carrier collection efficiency [43, 44]. Furthermore, the refractive index of Al2O3 lies between those of air and Si, making it suitable for optical impedance matching. Accordingly, a composite structure consisting of an Al2O3/SiNP array is investigated in this study, aiming to further reduce interfacial reflection by utilizing an effective refractive index gradient [10]. As anticipated, the average reflectance of the Al2O3/SiNP array is reduced to 3.61%, with a corresponding SWR of 2.94%, as illustrated by the blue curve in Fig. 2.

The plasmonic light trapping technology is another common anti-reflection technique besides nano-texturing. To investigate the anti-reflection properties of metal nanoparticle arrays, Fig. 3 shows the wavelength-dependent reflectance of AgNCs with different Inline graphic values deposited on a Si substrate. In our structure, when the incident light is polarized along the x-axis and propagates along the z-axis, the LSPR is primarily excited in the direction perpendicular to the cone axis (i.e., along the x-axis). The resonance wavelength strongly depends on the geometric characteristics of the AgNCs and the surrounding dielectric environment. Since the AgNC array is placed on a high refractive index Si substrate, this asymmetric environment causes a significant redshift of the dipole resonance position (not shown in the figure). The main reason for the reduction in reflectance due to LSPR can be easily understood from the graph, where the dips in the reflectance spectrum at the quadrupole resonance become broader and redshift as Inline graphic increases, leading to lower reflectance near the quadrupole resonance wavelength. As Inline graphic increases, the contact area between the AgNC array and the Si substrate [19] increases, resulting in weaker light coupling between the AgNC array and the substrate, which in turn increases the reflectance of light in the near-infrared region. This is further confirmed by the electric field distribution on the nanoparticle-air side, as shown in Fig. 7. Therefore, the deposition of AgNC array does not significantly improve the anti-reflection properties of Si substrate and may even have a negative effect.

Fig. 3.

Fig. 3

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The reflectivity curves of the AgNC array on a Si substrate with varying Inline graphic values, with the bare flat Si surface (black) as a reference

Fig. 7.

Fig. 7

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Electric field distributions of different configurations at wavelengths of 500 nm and 900 nm: (a, d) AgNC array, (b, e) AgNC–SiNP array, and (c, f) AgNC–Al2O3/SiNP array

The suboptimal anti-reflection properties of the AgNC array on a Si substrate can be improved by introducing the SiNP array. Figure 4 shows the wavelength-dependent reflectance spectra of AgNC–SiNP array on a Si substrate with different Inline graphic values, combining nano-texturing and plasmonic light trapping technologies. The black line represents the reflectance of the SiNP array deposited on a Si substrate. From the figure, it can be seen that within the visible light range, the reflectance of the AgNC–SiNP array decreases as Inline graphic increases.

Fig. 4.

Fig. 4

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The reflectance spectra of arrays composed of AgNCs with different Inline graphic values mounted on SiNPs (R = 175 nm, H1 = 100 nm)

As a Mie resonator, the field distribution of the cylindrical nanostructured SiNPs at resonance significantly overlaps with the Si substrate. This overlap not only leads to direct absorption of near-field energy by the substrate but also triggers energy dissipation radiating into the substrate, causing more light to be transmitted into the substrate and thus reducing reflectance. In addition to the reduction in reflectance from a single SiNP acting as a resonator, the entire SiNP array and the surrounding air gap, according to the effective refractive index theory, can be considered as a uniform thin film with a thickness of 100 nm and a refractive index of 2.35. Compared to direct light incidence on the Si substrate with n = 3.5, the effective refractive index of 2.35 serves as a transition, also contributing to the reduction in reflectance. Another reason for the decreased reflectance is that the AgNC in the structure of AgNC–SiNP array is effectively placed on a substrate with a refractive index of 2.35, rather than directly on the Si substrate, which shifts its dipole resonance toward the blue. This also causes some of the scattered light to couple into the substrate, leading to a further reduction in reflectance. By comparing Figs. 3 and 4, it can be observed that the AgNC–SiNP array significantly reduces the reflectance in the visible light range. In the near-infrared range, the introduction of the AgNC–SiNP array reduces the average reflectance of bare Si substrate from approximately 40% to around 10%.

It is well established that introducing a dielectric interlayer between metallic nanoparticles and the underlying substrate can effectively alter the scattering characteristics of the nanoparticles, thereby enhancing the coupling efficiency of scattered light into the substrate. To further enhance the anti-reflective performance of the Si surface, introducing a dielectric spacer layer into the AgNC–SiNP array represents a promising strategy. In this study, Al2O3, a commonly used material in photovoltaic devices, is employed as the dielectric layer. Figure 5 presents the reflectance spectra of AgNC–Al2O3/SiNP arrays with varying Inline graphic values as a function of wavelength. Overall, the reflectance of the AgNC–Al2O3/SiNP arrays is lower than that of the SiNP array across the entire wavelength range, except for the case with Inline graphic = 50 nm at around 555 nm, where a slight increase is observed. For the AgNC–Al2O3/SiNP array, when the wavelength exceeds 810 nm, larger Inline graphic values correspond to lower reflectance. In contrast, below 810 nm, the reflectance spectra for different Inline graphic values begin to overlap. Notably, the lowest SWR of 1.99% is achieved at Inline graphic = 30 nm, with a corresponding average reflectance of 2.60%. For comparison, the average reflectance of Ag nanospheres on Si pillar arrays is 2.66% [27], while the SWR for Al nanospheres on Si pillar arrays is 2.22% [28].

Fig. 5.

Fig. 5

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The reflectivity spectra of arrays composed of AgNCs with different Inline graphic values placed on Al2O3/SiNPs (R = 175 nm, H1 = 100 nm, H2 = 70 nm)

To investigate the underlying mechanism responsible for the anti-reflective performance of the AgNC–Al2O3/SiNP array, we analyze the scattering cross-section spectra of AgNCs with varying Inline graphic values, as shown in Fig. 6. Specifically, Fig. 6a shows the AgNC array on a Si substrate, while Fig. 6b illustrated the proposed configuration. A comparison between Figs. 6a and b reveals that, due to the Fano effect [45–47], the dipolar resonance of the AgNC–Al2O3/SiNP array exhibits a distinct blueshift relative to that of the AgNC array. This spectral shift facilitates stronger coupling of the incident light into the Si substrate. In contrast, quadrupolar resonances in the AgNC array configuration contribute significantly to the scattering response, but their higher-order nature makes them less effective at enhancing light–matter interactions, thereby reducing coupling efficiency with the substrate. The mechanism behind the Fano resonance in this structure mainly arises from the coherent interference between the sharp resonance mode of the AgNC array and the broadband scattering background of Al2O3/SiNPs. Due to the sharp tip of the AgNCs, they generate LSPR effect, characterized by a narrow spectrum and high intensity. In contrast, the Al2O3/SiNP array and the Si substrate form a broadband, continuous spectrum scattering background. When these two modes overlap in frequency, constructive and destructive interference occurs, resulting in a typical asymmetric line shape in the scattering spectrum, which is the Fano resonance. Furthermore, for a fixed Inline graphic, the scattering cross-section of the AgNC–Al2O3/SiNP array is consistently larger than that of the AgNC array, indicating enhanced light coupling into the substrate and consequently reduced surface reflectance. The trend observed in the scattering cross-section is consistent with the reflectance variations shown in Figs. 3a and 5a, thereby validating the significantly improved anti-reflection performance of the AgNC–Al2O3/SiNP array.

Fig. 6.

Fig. 6

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a Scattering cross-section curves of AgNCs with varying sizes deposited on a Si substrate and b on Al2O3/SiNPs

In addition to the scattering cross-section analysis, Fig. 7 presents the electric field distributions in the y–z plane at wavelengths of 500 nm (top row) and 900 nm (bottom row) for three configurations: a bare AgNC array, an AgNC–SiNP array, and an AgNC–Al2O3/SiNP array, with Inline graphic fixed at 90 nm. As shown in Fig. 7a and d, for the AgNC array alone, the electric field is primarily concentrated along the lateral surfaces of the cones, resulting in a larger proportion of incident light being reflected back into the air and consequently higher reflectance. Since 500 nm is closer to the resonance wavelength (428 nm), more incident light is coupled into the substrate, which explains the lower reflectance observed at 500 nm compared to that at 900 nm, as indicated by the cyan curve in Fig. 3. Upon introducing the SiNP array (Fig. 7b and e), the electric field intensity along the cone sidewalls decreases, while the field coupling across the air gaps between neighboring nanopillars becomes significantly enhanced. This leads to a notable reduction in reflectance compared to the AgNC array alone. When the Al2O3 layer is further incorporated (Fig. 7c and f), strong field localization occurs near the base edges of the nanocones at both 500 nm and 900 nm. The significantly enhanced electric field at this interface promotes more efficient light–matter interaction, facilitating greater light coupling into the substrate and thereby reducing surface reflection.

The LSPR effect of metallic nanoparticles is influenced not only by particle shape but also by the intrinsic optical properties of the constituent materials [48–51]. As demonstrated in the preceding analysis, through the introduction of an Al2O dielectric layer, the AgNC–Al2O3/SiNP array exhibits superior anti-reflection performance compared to the Ag nanosphere–SiNP array configuration. As an extension of the Ag-based composite structure, this study investigates the anti-reflective properties of three alternative metal nanocone configurations integrated with Al2O3/SiNP arrays. The anti-reflection factor is defined as the ratio of the reflectance of the metallic nanocone–Al2O3/SiNP array to that of the Al2O3/SiNP array without metallic nanocones. Figure 8a presents the anti-reflection factor spectra of four metal-based hybrid structures (AlNC–Al2O3/SiNP array, CuNC–Al2O3/SiNP array, AgNC–Al2O3/SiNP array, and AuNC–Al2O3/SiNP array) with a fixed Inline graphic of 30 nm.

Fig. 8.

Fig. 8

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Anti-reflection factor spectra of four hybrid metal nanocone–Al2O3/SiNP arrays, a at a fixed Inline graphic of 30 nm and b at their respective optimal Inline graphic values

The results indicate that, due to the combined effects of nanocone-induced scattering, the graded effective refractive index of the Al2O3/SiNP array, and enhanced light trapping via multiple reflections, all four metal–dielectric hybrid structures exhibit excellent anti-reflection performance, with average reflectance of 2.73%, 2.52%, 2.60%, and 2.55% and corresponding SWR of 2.11%, 1.86%, 1.99%, and 1.94%, respectively. Remarkably, the CuNC–Al2O3/SiNP array exhibits consistent suppression of reflection over nearly the entire spectral range. Furthermore, in the near-infrared region, the anti-reflective performances of all four metal-based composite structures tend to converge, with each configuration exhibiting superior performance compared to the Al2O3/SiNP array alone. Figure 8b compares the anti-reflection factors of the four hybrid structures at their respective optimized nanocone sizes, with the optimal Inline graphic being 31.8 nm (Al), 35.7 nm (Cu), 30 nm (Ag), and 35.3 nm (Au). The corresponding average reflectance values are 2.70%, 2.27%, 2.60%, and 2.42%, and the SWR values are 2.10%, 1.66%, 1.99%, and 1.87%, respectively. These results demonstrate that the CuNC–Al2O3/SiNP array achieves superior antireflection performance relative to its Al, Ag, and Au counterparts. Based on the simulation results, CuNC–Al2O3/SiNP array exhibits the best anti-reflection performance due to their maximum parasitic absorption, with an average absorption rate of 6.14%. As the primary operating wavelengths for all four metals fall within the visible light range, CuNCs, due to their stronger interband transitions, generate a broader and more strongly damped LSPR in the visible light region, leading to higher dissipation. In the near-infrared region, the optical constants of all metals gradually converge, causing the LSPR effect to weaken and their reflection behavior to become more similar.

Finally, we briefly discuss the fabrication feasibility of the proposed AgNC–Al2O3/SiNP array. With the advancement of micro- and nanofabrication technologies [52], the designed structure can be realistically implemented using a sequential combination of top-down and bottom-up approaches. SiNPs are first patterned on a silicon substrate through electron beam lithography (EBL) followed by inductively coupled plasma (ICP) etching. Conformal Al2O3 cylinders are then deposited via atomic layer deposition (ALD) and anisotropically etched to form well-defined coaxial geometries. Finally, AgNCs are fabricated on top of the Al2O3 pillars using either EBL combined with angled metal deposition and lift-off, or template-assisted physical vapor deposition.

Conclusion

A two-dimensional periodic array of AgNCs–Al2O3/SiNPs deposited on semiconductors substrate is designed, and its anti-reflection characteristics are studied with FDTD method in this paper. The results show that the average reflectance and SWR of AgNC–Al2O3/SiNP array are as low as 2.60% and 1.99%, respectively, over the broadband spectral range of 400–1100 nm. To elucidate the underlying anti-reflection mechanism, the reflectance properties of individual and combined structures—including the SiNP array, Al2O3/SiNP array, AgNC array, AgNC–SiNP array, and the AgNC–Al2O3/SiNP array—are systematically investigated. The synergistic effects of the tunable forward scattering of Ag nanocones, the inherent anti-reflective properties of the SiNP array, and the refractive index matching provided by the Al2O3 layer collectively enhance the anti-reflection performance of the proposed structure. Through parameter optimization involving five geometric variables, the structure with AgNCs of Inline graphic = 30 nm placed atop an Al2O3/SiNP array (H1 = 100 nm, H2 = 70 nm, R = 175 nm, P = 400 nm) achieves the lowest SWR among all evaluated configurations. Extending beyond Ag-based system, this study also evaluates the anti-reflection performance of composite structures incorporating Al-, Cu-, and Au-nanocones, respectively. While the CuNC–Al2O3/SiNP array demonstrates the lowest average reflectance and SWR, the AgNC–Al2O3/SiNP array emerges as the most promising candidate for broadband antireflection applications, owing to the high oxidation tendency of Al and Cu, as well as the high material cost of Au.

Acknowledgements

The authors would like to thank the College of Science at Northwest A&F University for providing the necessary facilities and resources to carry out this work.

Author contributions

Luo XY. Sun W. Xiong ZC. and Chang Y.: investigation; simulation work; drafting the manuscript. An XY. Ren WY. Wang H.: data analysis and interpretation. An HC.: review & editing; supervision.

Funding

This work was supported by the Ph.D. Early Development Program of Northwest A&F University (Grant No. Z109022017/2020) and the College Students Innovation and Entrepreneurship Training Program of Northwest A&F University (Grant No. X202410712673).

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Footnotes

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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