# Design of a Highly Efficient Subwavelength Antireflective Structure for Solar Cells

Authors: Lin Chen; Zhao Huang
Journal: International Journal of Optics
 (2022)

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## Abstract

An efficient optical antireflective (AR) structure plays a vital role in high-performance thin-film solar cells. Here, we design a surface relief AR structure consisting of a two-dimensional (2D) array of a subwavelength ring and pillar-shaped feature, capable of suppressing optical reflection over a wide spectral window of the solar spectrum. Our simulations show that the weighted average reflectance of the subwavelength AR structure is as low as 4.2% in the 400–1100 nm spectral range in the normal incidence condition and almost 10-fold reduction compared with a bare silicon surface. When placed on the front side of a simple Si thin-film photovoltaic solar cell, this subwavelength AR structure leads to an improved light absorption with simulated results showing an increase of 53% short-circuit current compared to a flat solar cell. Besides, our simulations show that this AR structure could, in principle, perform well against reasonable fabrication errors.


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## Body

## 1. Introduction

With the degradation of the environment and climate change on earth, renewable energy has become a key theme in sustainable social development. In the past decades, photovoltaic technology has attracted much attention for its potential to provide renewable energy instead of traditional fossil fuels [1–3]. While there is a growing trend of this technology being deployed in industrial environments, its cost is still one of the main factors limiting worldwide civil end use [4]. One potential way to reduce the cost is to increase photovoltaic solar cells’ efficiency by reducing the reflection of solar cells and increasing their absorption [5, 6]. In this research direction, several methods are commonly used for reducing the unwanted Fresnel reflection on the surface between two adjacent materials with different refractive indices, such as single or multiple-layer antireflective (AR) coatings [7, 8] and light-trapping nanostructures [9]. It is well-known that a single λ/4 thick dielectric layer will significantly reduce Fresnel reflection by realizing destructive interference at the reflection path over a narrow spectral bandwidth centered at λ. Although applying multiple layers can broaden the antireflection spectral window [10], it is difficult to find proper material combinations and grow perfect multilayers at a low cost. Alternatively, moth-eye structure and regular or random pyramids can be used in solar cells to improve light absorption efficiency [11, 12] because they increase effective optical scattering paths to allow more photons to be absorbed. They are often used in wafer-based silicon solar cells, which have a typical active layer thickness on the order of 10 μm. However, typical thin-film silicon solar cells only have a thickness of about 3 μm. As a result, these light-trapping structures are not suitable [13]. Because of their tailored optical responses, subwavelength structures have attracted much attention in designing antireflective surfaces. For example, Spinelli et al. presented a new concept to suppress the reflection of light from a silicon surface in the 450–900 nm spectral range [14] using a very simple nanostructure. Along this direction, there have been many proposed and demonstrated outstanding absorption enhancing nanostructures, for instance, tungsten elliptical arrays on monolayer molybdenum disulfide, trapezoid-pyramidal structure-based PEDOT: PSS/c-Ge, Ag nanoparticles, and TiO2-inverted triangular prism, Ti ring on SiO2-Si3N4-Ti thin films [15–19]. Notice that these nanostructures all require heterogeneous integration of exterior materials, complicating the device fabrication processes and potentially defeats the purpose of lowering the solar cells’ cost. A straightforward solution to bypass these issues could be surface engineering the solar cell by directly patterning the thin-film silicon layer.In this study, a broadband surface relief subwavelength AR structure for thin-film silicon solar cells is designed and optimized. It consists of a two-dimensional (2D) array of rings and pillars. Its weighted average reflectance is as low as 4.2% over the 400–1100 nm spectral range, which is almost an order of magnitude reduction compared with a bare silicon surface. The directivity of the antireflection and polarization sensitivity of this structure are further studied in detail. Besides, our investigation on the light absorption property of a 3μm thick thin-film silicon solar cell suggests that the generated short-circuit current of a simple but representative solar cell can be improved by more than 50%. Finally, the fabrication tolerance analysis shows that our subwavelength AR structure can have geometric tolerance to a certain extend.


## 2. Results and Discussion

Figure1 shows the schematic view and the section view of the proposed subwavelength AR structure. It is a periodic structure that can be integrated onto the surface of the top silicon layer of solar cells. Its unit cell consists of an outer ring and a middle pillar. The outer and the inner diameters of the ring structure are dout and din, respectively. The diameter of the pillar is dcore. The outer ring and the middle pillar have the same height, h. Moreover, the periods in the x and y directions are the same and are fixed at p=500nm.Figure 1
(a) Schematic view of the silicon subwavelength AR structure used in the simulations. (b) Main geometric parameters of the silicon subwavelength AR structure. (c) Normalized scattering cross-section (inset: normalized intensity profile at the resonance wavelength).
(a)(b)(c)To minimize the reflection over a wide wavelength range, it is crucial to find the optimum geometric parameters of the subwavelength AR structure. We use the averaged reflectance,Rave, weighted with the AM1.5 solar spectrum in the 400–1100 nm spectral range, as a quantitative figure of metric for the optimization design. It is defined as follows:(1)Rave=∫4001100Rλ×ΦAM1.5dλ∫4001100ΦAM1.5dλ,where λ is the wavelength of the incident light, R(λ) is the corresponding wavelength-dependent reflectance of the front surface of solar cells, and 400 nm and 1100 nm are the lower and upper boundaries of the absorption wavelength of interest for the silicon solar cells. The electromagnetic response of this structure is simulated using commercially available finite-difference time-domain (FDTD) tools. A simulation domain of 0.5 × 0.5 × 1 μm (x × y × z) is used with periodic boundary conditions in the x and y directions and a perfectly matched layer condition in the z-direction. The light source is a broadband (400–1100 nm) plane wave with a varying angle of incidence to the substrate. After checking the numerical convergence, the simulation mesh grid is set to 10 nm over the entire simulation domain, with a refined override setting of 5 nm over the region occupied by the subwavelength ring and pillar. The optical dispersion property of silicon is taken into account in all numerical simulations [20]. Our investigation using particle swarm optimization yields the following main geometric parameters of the optimized subwavelength AR structure, as given in Table 1. The scattering cross-section of its unit is analyzed [14], and the corresponding result is shown in Figure 1(c). It suggests that this structure has a greatly enhanced normalized scattering cross-section across the whole spectrum of interest (400–1100 nm). The peak of the scattering cross-section is about ten times the geometric cross-section at the wavelength of 655 nm, which is near the peak wavelength of the solar spectrum. Also, from the inset of Figure 1(c), there is a strong leaky channel into the silicon substrate. These factors are mainly responsible for the reduced reflection and enhanced absorption in the photovoltaic solar cell.Table 1
The main geometric parameters of the subwavelength AR structure (μm).
dcoredindouthPeriod0.060.3330.440.1550.5Figure2(a) shows the simulated reflectance spectra of a silicon substrate with our optimized AR structure under normal incidence. The result suggests that the reflectance varies only slightly with the wavelength, and for the entire spectrum from 400 nm to 1100 nm, it is well below 10%. The reflectance from a bare flat silicon substrate is also simulated and shown as the black curve for comparison. It has a minimum value of 30%, far exceeding that of our subwavelength structure. According to equation (1), the weight reflectance, Rave, over the entire spectral window for our case is less than 4%. It strongly indicates that this kind of surface structure is beneficial in suppressing optical reflection. The trend shown here agrees well with reports elsewhere [21].Figure 2
(a) Reflectance spectra of the silicon substrate with and without AR subwavelength structures under normal incidence. (b) Reflectance for s-polarized (black curve with solid square symbols) and p-polarized (red curve with solid dot symbols) incident beam over the angle of incidence (AOI) from 10° to 60°.
(a)(b)For the photovoltaic application, an AR optical structure must show low reflectance over a wide range of incident angles for both polarizations. Figure2(b) shows the weighted averaged reflectance Rave simulated for s-polarized (black curve with solid square symbols) and p-polarized (red curve with solid dot symbols) light over the 400–1100 nm spectral window as a function of the angle of incidence (AOI) from 10° to 60°. Overall, the reflectance for s and p-polarizations increases gradually with the angle of incidence. The reflectance, however, remains below 10% for both s and p-polarizations for the incident angle up to 30°. Moreover, the averaged reflectivity for p-polarization is slightly larger than that for s-polarization at large angles suggesting our subwavelength structure shows a mild polarization dependence for s and p-polarizations.To examine our subwavelength AR structure’s efficacy, a simple three-layer Si thin-film solar cell is modeled. It consists of an active layer of a 3μm thickness c-Si, sandwiched by the subwavelength AR structure on the top and a 0.5 μm Al slab at the bottom. The absorbed optical energy is first calculated to study the photocurrent in the solar cell. The absorbed energy density per unit volume of the active layer, Pabs, could be derived from the following formula:(2)Pabs=−0.5ωE⟶2imagε,where ω is the incident light’s angular frequency, E⟶ is the electric field, and imag(ε) is the imaginary part of the permittivity. Figure 3 shows the calculated results of the spatial distribution of Pabs at the wavelength of 600 nm and 1100 nm, respectively. In the first case, the absorption occurs strongly in the whole Si active layer underneath the subwavelength AR structure. In the latter case, the spatial absorption is much lower in the Si active layer. These results agree well with the absorption spectra above. Besides, we also see an interference pattern due to backward reflections at the interfaces, thereby increasing the effective optical path and light absorption.Figure 3
The spatial absorption profiles at 600 nm (a) and 1100 nm (b).
(a)(b)To roughly estimate the enhancement of photocurrent with our proposed AR structures, we assume an ideal extraction of charged carriers, and all electron-hole pairs contribute to the photocurrent in both cases with and without AR structures. The short-circuit current densityJsc under the standard solar irradiance can be calculated according to reference [22], using the following two equations:(3)QEλ=PabsλPinλ,Jsc=e∫λhcQEλIAM1.5λdλ,where e is the charge of an electron, h is Plank’s constant, c is the speed of light in the free space, and IAM1.5(λ) is the AM 1.5 solar spectrum. Our calculation shows that Jsc is around 28.6 mA/cm2 with a 53% increment compared to a device without an AR layer (18.7 mA/cm2).Fabrication tolerance plays a vital role in the performance of the subwavelength structures. To study the fabrication tolerance of the proposed subwavelength AR structure, the performance of Si subwavelength AR structure under different degrees of size deviation is simulated. Fabrication variations of the AR structure’s outer ring and middle pillar are considered. Especially, the impact of the deviation of their diameters and the sidewall angles from the optimal values is studied. The simulated results for weighted reflectance with the AM1.5 solar spectrum are shown in Figures4(a) and 4(b), respectively. Noticeably, the results show very slight degradation of the reflectance within the variation range of ±10 nm and 0–10°, respectively. Therefore, our proposed AR structures could in principle perform well against minor fabrication errors.Figure 4
Effect of fabrication variations of the middle pillar (a) and outer ring (b) on the reflectance.
(a)(b)


## 3. Conclusion

We have proposed a unique subwavelength structure composed of pillars and rings that can largely suppress the Si surface’s reflection across a broadband wavelength range. Our simulations show that the averaged reflectance, weighted with the AM1.5 solar spectrum in the 400–1100 nm spectral range, can be reduced from 35% down to only 4.2%. Notably, the modeled short-circuit current for a simple thin-film solar cell exhibits a 53% increment compared to that of a device without the AR layer. Besides, we show that the subwavelength AR structures are robust to certain degrees of fabrication errors. The results demonstrated here provide a straightforward and low-cost method, feasible with the current nanoimprinting technology, for fully exploring the advantages of thin-film solar cells.



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*Source: 9963336-2022-02-07.xml*