Light Reﬂection Loss Reduction by Nano-Structured Gratings for Highly E ﬃ cient Next-Generation GaAs Solar Cells

: This paper mainly focuses on increasing the conversion e ﬃ ciency of GaAs solar cells by reducing the light reﬂection losses. The design of nano-structured gratings and their light trapping performance are modelled and optimised by using the ﬁnite-di ﬀ erence time-domain (FDTD) method. The sunlight directly impinges on the solar panel or cells, then a portion of the incident sunlight reﬂects back to the air from the surface of the panel, thus leading to a reduction in the light absorption capacity of the solar cells. In order to proliferate the light absorption capacity of solar cells nano-grating structures are employed, as they are highly capable of capturing the incident sunlight compared to a conventional (or ﬂat type) solar cell, which results in generating more electrical energy. In this study, we design three di ﬀ erent types of nano-grating structures, optimise their parameters and their performance in light capturing capacity. From the simulation results, we conﬁrm that that it is possible to reduce light reﬂection losses up to 27%, by using the nano-grating structures, compared to conventional type solar cells. This reduction of reﬂection losses helps to improve the conversion e ﬃ ciency of next-generation GaAs solar cells signiﬁcantly for a sustainable green Earth.


Introduction
According to the latest report published by the United Nations Department of Economic and Social Affairs (UN DESA), the world population is expected to increase by 2 billion within the next 30 years. The growth rate of world population indicates that the current world population could jump from 7.7 billion (currently) to 9.7 billion by 2050, and it is also projected to have a peak of approximately 11 billion by 2100 [1]. For this large number of populations, besides all the fundamental needs, there will be a huge demand for energy and meeting that energy demand will be a key challenge and big obstacle towards dreaming of a sustainable green globe. Currently, of the global energy demand, the majority of energy generation is fossil fuels based, which is supposed to be running out very rapidly. Additionally, to restrain the carbon dioxide (CO 2 ) concentration in the air, it is necessary to reduce the energy harvest from burning fossil fuels by up to 3 TW within the next 25 years and to produce the rest of the required energy from renewable energy sources [2][3][4]. However, as an alternative to fossil nano-grating structures, such as triangular, trapezoidal (hatch top or truncated cone), and rectangular shapes. The nano-gratings' height and aspect ratio were varied during the simulation process in order to find the best conditions for capturing more of the incident light into the GaAs substrate, for high conversion efficiency of solar cells. The computation was based on the principle of FDTD method, i.e., a mesh grid network, and Maxwell's equations [59,60]. The performance of nano-grating structures was simulated and their properties (light transmission, reflection, and absorption rates) were evaluated by considering the grating shapes, design aspect ratio, and the field components distribution as well.
This paper is organised as follows. Section 2 briefly describes the properties of moth's eye light collection ability, characteristics of an anti-refractive coating layer, and the geometry design for different types of nano-grating shapes. Section 3 describes the simulation results and discussion, followed by a conclusion in Section 4.

Principle of Moth's-Eye
An efficient solar cell has to reflect the minimum and absorb the maximum amount of the incident light. The use of an AR structure was inspired by the natural model of moth's eyes [61,62]. Japanese researchers initially found that this useful property exists in nature's intelligent creature: moth's eyes. Hence, they made an antireflective film coating on solar panels for better utilisation of sunlight.
The moth-eye film was produced by Noboru Yamada, a researcher at the Nagaoka University of Technology, Japan, who worked in research collaboration with analysts at Mitsubishi Rayon Co., Ltd. Tokyo, Japan, and Tokyo Metropolitan University, Tokyo, Japan [63]. Utilising anodic permeable alumina molds, they were able to nano-imprint the micro-structure of moth's eyes into a form of resin, and this gave a high efficiency, extensive range, and straightforward technique for producing the AR layer. These "moth eye" structures are commonly known as antireflective subwavelength structures (SWSs) that can effectively suppress the reflection in broadband and omni-directional ranges. Successful fabrications of these types of antireflective SWSs using various physical vapor nano/micro fabrication processes are reported in the literature [59,[61][62][63][64]. Figure 1 shows an example of the nanoscopic structure of a Moth's eye [65]. Based on the outcome of various tests conducted on a silicon solar panel coated with this resin, they concluded that use of this thin film can improve the light absorption properties compared with the conventional solar panel.
Energies 2020, 13, x FOR PEER REVIEW 3 of 12 The finite-difference time-domain (FDTD) simulation tool is used to design, model, and analyse the properties of nano-grating structures. For this simulation, we considered three different types of nano-grating structures, such as triangular, trapezoidal (hatch top or truncated cone), and rectangular shapes. The nano-gratings' height and aspect ratio were varied during the simulation process in order to find the best conditions for capturing more of the incident light into the GaAs substrate, for high conversion efficiency of solar cells. The computation was based on the principle of FDTD method, i.e., a mesh grid network, and Maxwell's equations [59,60]. The performance of nano-grating structures was simulated and their properties (light transmission, reflection, and absorption rates) were evaluated by considering the grating shapes, design aspect ratio, and the field components distribution as well.
This paper is organised as follows. Section 2 briefly describes the properties of moth's eye light collection ability, characteristics of an anti-refractive coating layer, and the geometry design for different types of nano-grating shapes. Section 3 describes the simulation results and discussion, followed by a conclusion in Section 4.

Principle of Moth's-Eye
An efficient solar cell has to reflect the minimum and absorb the maximum amount of the incident light. The use of an AR structure was inspired by the natural model of moth's eyes [61,62]. Japanese researchers initially found that this useful property exists in nature's intelligent creature: moth's eyes. Hence, they made an antireflective film coating on solar panels for better utilisation of sunlight.
The moth-eye film was produced by Noboru Yamada, a researcher at the Nagaoka University of Technology, Japan, who worked in research collaboration with analysts at Mitsubishi Rayon Co. Ltd. Tokyo, Japan, and Tokyo Metropolitan University, Tokyo, Japan [63]. Utilising anodic permeable alumina molds, they were able to nano-imprint the micro-structure of moth's eyes into a form of resin, and this gave a high efficiency, extensive range, and straightforward technique for producing the AR layer. These "moth eye" structures are commonly known as antireflective subwavelength structures (SWSs) that can effectively suppress the reflection in broadband and omni-directional ranges. Successful fabrications of these types of antireflective SWSs using various physical vapor nano/micro fabrication processes are reported in the literature [59,[61][62][63][64]. Figure 1 shows an example of the nanoscopic structure of a Moth's eye [65]. Based on the outcome of various tests conducted on a silicon solar panel coated with this resin, they concluded that use of this thin film can improve the light absorption properties compared with the conventional solar panel. Figure 1. The nanoscopic structure of a moth's eye [65]. The surface of the Moth's eye structure results in broadband anti-reflection effects, due to its nature of refractive indices changes between the media.

Antireflection Coating
As mentioned, the efficiency of solar cells can be increased using an anti-reflection coating, which reduces the amount of light reflection for certain ranges of wavelength. The minimum reflectance can be calculated for different polarisations, namely, s-polarisation and p-polarisation, as shown in the following Equations (1) and (2). R S = ((n 1 Cosθ 1 − n 2 Cosθ 2 )/(n 1 Cosθ 1 + n 2 Cosθ 2 )) 2 (1) R P = ((n 1 Cosθ 2 − n 2 Cosθ 1 )/(n 1 Cosθ 2 + n 2 Cosθ 1 )) 2 (2) where, n 1 and n 2 represent the refractive indices of media 1 and 2 which are air and GaAs. θ 1 and θ 2 represent the angle of incidence and angle of refraction, respectively. λ 1 and λ 2 represent the wavelength of incident medium M 1 and refracted medium M 2 , as shown in Figure 2.
The nanoscopic structure of a moth's eye [65]. The surface of the Moth's eye structure results in broadband anti-reflection effects, due to its nature of refractive indices changes between the media.

Antireflection Coating
As mentioned, the efficiency of solar cells can be increased using an anti-reflection coating, which reduces the amount of light reflection for certain ranges of wavelength. The minimum reflectance can be calculated for different polarisations, namely, s-polarisation and p-polarisation, as shown in the following Equations (1) and (2). 2 (1) where, n1 and n2 represent the refractive indices of media 1 and 2 which are air and GaAs. θ1 and θ2 represent the angle of incidence and angle of refraction, respectively. λ1 and λ2 represent the wavelength of incident medium M1 and refracted medium M2, as shown in Figure 2. On the other hand, for an unpolarised light, the total reflection coefficient can be explained as follows [66]: Furthermore, Figure 2 describes the relationship between the angle of incidence and angle of refraction using Snell's law. It represents the light reflection diagram of flat GaAs substrate. The incident light angle (θ1) is the angle between the incident ray and the surface normal. The refracted light angle (θ2) is the angle between the refracted ray and the surface normal. When the light is near normal incidence, for both polarizations, the reflection coefficient using Fresnel equation can be given by [67]: On the other hand, for an unpolarised light, the total reflection coefficient can be explained as follows [66]: Furthermore, Figure 2 describes the relationship between the angle of incidence and angle of refraction using Snell's law. It represents the light reflection diagram of flat GaAs substrate. The incident light angle (θ 1 ) is the angle between the incident ray and the surface normal. The refracted light angle (θ 2 ) is the angle between the refracted ray and the surface normal. When the light is near normal incidence, for both polarizations, the reflection coefficient using Fresnel equation can be given by [67]: R total = R S = R P = ((n 1 − n 2 )/((n 1 + n 2 )) 2 (4)

Different Types of Nano-Grating Shapes
In this section, we present the concept of nano-grating shapes. The modeled nano-grating shapes are: (i) rectangular, (ii) trapezoidal with 0.5 aspect ratio, and (iii) triangular. The aspect ratio is defined as the proportion of the top base width (a) over the bottom base (b) of a trapezoid, triangle, or rectangle Energies 2020, 13, 4198 5 of 12 nano-grating (i.e., a/b), as can be seen in Figure 3. These geometries are represented in Figure 3. Different shapes' effect on the light reflection and light trapping behavior of nano-structures has been an interesting topic for researchers [68,69]. We investigated different shapes to confirm that having inclined walls for nano-structures provides a better AR coating. Rtotal = RS = RP = ((n1 -n2) / ((n1 + n2)) 2 (4)

Different Types of Nano-Grating Shapes
In this section, we present the concept of nano-grating shapes. The modeled nano-grating shapes are: (i) rectangular, (ii) trapezoidal with 0.5 aspect ratio, and (iii) triangular. The aspect ratio is defined as the proportion of the top base width (a) over the bottom base (b) of a trapezoid, triangle, or rectangle nano-grating (i.e., a/b), as can be seen in Fig. 3. These geometries are represented in Figure 3. Different shapes' effect on the light reflection and light trapping behavior of nano-structures has been an interesting topic for researchers [68,69]. We investigated different shapes to confirm that having inclined walls for nano-structures provides a better AR coating.

Simulation Results and Discussion
Based on the properties of light reflection and light absorption rates, the simulation results of different nano-grating structures are discussed in this section. Opti-FDTD (which works based on Maxwell's equation) software package was used in this work to perform the diffractive optics simulation. This commercially available software package is versatile and capable of modeling and mixing up various elements, such as the light propagation, scattering and diffraction, reflection and polarisation impacts. It can likewise demonstrate material anisotropy and scatter, with no pre-supposition of field conduct, for example the gradually differing amplitude estimation. The method takes into consideration the compelling and examination of sub-micron i.e., nano-scale devices, with the finest structures over any wavelength and feature size, and with any type of structure, such as, regular or irregular shapes. The advanced computing technologies help to minimise the existing limitations of conventional FDTD method, related to handle dispersion with some metal components, or when modeling some subwavelength size structures. Figure 4 present the specific designs for the modelling of triangular, trapezoidal, and rectangular-shaped nano-gratings. The aspect ratio for the triangular-shaped nano-grating was zero (0), while for the rectangular-shaped nano-grating it was one (1). These shapes, along with the trapezoidal-shaped nano-gratings with the aspect ratio of 0.5, were used in the simulation, and for analysis of the light reflection, transmission, and absorption behavior of the SWG structures in solar cells. The two-dimensional FDTD mesh cell size for this study was 5 nm, and a time step of 0.1/s was used. As shown in Figure 4, two lines were designed above the design structures, i.e., red and green lines. The red represents the incident line as sunlight that impinges on the grating zone, and the reflected light can be calculated at the green line (i.e., the light reflection losses). Moreover, there are

Simulation Results and Discussion
Based on the properties of light reflection and light absorption rates, the simulation results of different nano-grating structures are discussed in this section. Opti-FDTD (which works based on Maxwell's equation) software package was used in this work to perform the diffractive optics simulation. This commercially available software package is versatile and capable of modeling and mixing up various elements, such as the light propagation, scattering and diffraction, reflection and polarisation impacts. It can likewise demonstrate material anisotropy and scatter, with no pre-supposition of field conduct, for example the gradually differing amplitude estimation. The method takes into consideration the compelling and examination of sub-micron i.e., nano-scale devices, with the finest structures over any wavelength and feature size, and with any type of structure, such as, regular or irregular shapes. The advanced computing technologies help to minimise the existing limitations of conventional FDTD method, related to handle dispersion with some metal components, or when modeling some subwavelength size structures. Figure 4 present the specific designs for the modelling of triangular, trapezoidal, and rectangularshaped nano-gratings. The aspect ratio for the triangular-shaped nano-grating was zero (0), while for the rectangular-shaped nano-grating it was one (1). These shapes, along with the trapezoidal-shaped nano-gratings with the aspect ratio of 0.5, were used in the simulation, and for analysis of the light reflection, transmission, and absorption behavior of the SWG structures in solar cells. The two-dimensional FDTD mesh cell size for this study was 5 nm, and a time step of 0.1/s was used. As shown in Figure 4, two lines were designed above the design structures, i.e., red and green lines. The red represents the incident line as sunlight that impinges on the grating zone, and the reflected light can be calculated at the green line (i.e., the light reflection losses). Moreover, there are two more lines defined in the substrate which represent the transmission lines 1 and 2 (i.e., the amount of light transmitted into the GaAs substrate). The nano-structured gratings were designed on a GaAs substrate. For these simulations, the incident light wavelength and the nano-grating period were both kept constant at 830 nm. The grating height that describes the height of the nano-grating structure from the base surface to the upper surface, was kept from 0.05 µm to 0.4 µm.
Energies 2020, 13, 4198 6 of 12 two more lines defined in the substrate which represent the transmission lines 1 and 2 (i.e., the amount of light transmitted into the GaAs substrate). The nano-structured gratings were designed on a GaAs substrate. For these simulations, the incident light wavelength and the nano-grating period were both kept constant at 830 nm. The grating height that describes the height of the nano-grating structure from the base surface to the upper surface, was kept from 0.05 µm to 0.4 µm. Figure 4. Simulation plane diagrams of (a) triangular-shaped nano-gratings with the aspect ratio of zero, (b) trapezoidal-shaped nano-gratings with the aspect ratio of 0.5 and (c) rectangular-shaped nano-gratings with the aspect ratio of one, on top of the semiconductor (GaAs) substrates. Figure 5a,b show the light reflection and transmission spectra for triangular-shaped nano-gratings in the range of wavelengths from 0.75-µm to 1.05-µm. In this work, the wavelength range 0.75-1.05 µm was considered by keeping in mind that the saturation property of the GaAs, as described in Reference [70]. The grating heights were varied from 100 nm to 400 nm. It was confirmed that an increase in nano-grating height leads to a reduction in light reflection, and this trend was satisfied for all nano-grating heights, with reflection amount saturates in the range of 300 nm~350 nm. The simulated results show that when the nano-grating height was ~300 nm, the reflection loss was minimum. Figure 5c shows the light absorption rate for triangular-shaped nano-gratings. The simulated results confirmed that with the increase in nano-grating heights the light absorption increased and reached saturation when the height was around 300 nm~400 nm. The light absorption data were accounted using the obtained light reflection and light transmission data by following a simple formula, as written below: Figure 4. Simulation plane diagrams of (a) triangular-shaped nano-gratings with the aspect ratio of zero, (b) trapezoidal-shaped nano-gratings with the aspect ratio of 0.5 and (c) rectangular-shaped nano-gratings with the aspect ratio of one, on top of the semiconductor (GaAs) substrates. Figure 5a,b show the light reflection and transmission spectra for triangular-shaped nano-gratings in the range of wavelengths from 0.75-µm to 1.05-µm. In this work, the wavelength range 0.75-1.05 µm was considered by keeping in mind that the saturation property of the GaAs, as described in Reference [70]. The grating heights were varied from 100 nm to 400 nm. It was confirmed that an increase in nano-grating height leads to a reduction in light reflection, and this trend was satisfied for all nano-grating heights, with reflection amount saturates in the range of 300 nm~350 nm. The simulated results show that when the nano-grating height was~300 nm, the reflection loss was minimum. Figure 5c shows the light absorption rate for triangular-shaped nano-gratings. The simulated results confirmed that with the increase in nano-grating heights the light absorption increased and reached saturation when the height was around 300 nm~400 nm. The light absorption data were accounted using the obtained light reflection and light transmission data by following a simple formula, as written below: where L A represents the rate of light absorption, L R represents the rate of light reflection, and L T represents the rate of light transmission.
where LA represents the rate of light absorption, LR represents the rate of light reflection, and LT represents the rate of light transmission. The obtained light reflection and transmission spectra for trapezoidal-shaped nano-gratings are presented in Figure 6a,b. When the nano-grating height increased, the light reflection decreased and reached saturation around 200 nm~250 nm. It was evident that when the nano-gratings height was ~200 nm, the reflection loss was minimum. Figure 6c shows the light absorption rate for trapezoidal-shaped nano-grating structures with different heights ranging from 100 nm to 400 nm. As we expected, with increasing the nano-gratings height, the light absorption increased and reached saturation around 200 nm~300 nm. It was also clear that at the wavelength of 830 nm, the light absorption rate for 200 nm and 250 nm was very close. The capacity of light absorption increased gradually when the nano-grating height became larger. The obtained light reflection and transmission spectra for trapezoidal-shaped nano-gratings are presented in Figure 6a,b. When the nano-grating height increased, the light reflection decreased and reached saturation around 200 nm~250 nm. It was evident that when the nano-gratings height was~200 nm, the reflection loss was minimum. Figure 6c shows the light absorption rate for trapezoidal-shaped nano-grating structures with different heights ranging from 100 nm to 400 nm. As we expected, with increasing the nano-gratings height, the light absorption increased and reached saturation around 200 nm~300 nm. It was also clear that at the wavelength of 830 nm, the light absorption rate for 200 nm and 250 nm was very close. The capacity of light absorption increased gradually when the nano-grating height became larger. Figure 7a,b show the light reflection and transmission spectra for rectangular-shaped nano-gratings with the nano-grating heights ranging from 100 nm to 400 nm. The simulation results confirmed that the light reflection reduced with increasing the height and reached saturation around 200~250 nm. The reflection loss was minimum when the nano-grating height was~200 nm. The light absorption curves for the rectangular-shaped nano-grating structures, for different grating heights from 100 nm to 400 nm, are shown in Figure 7c. This structure also represented the saturation of absorbed light around 250 nm~300 nm, and the capacity of light absorption decreased gradually afterwards, with decreasing nano-grating heights. The simulation results presented in this paper are in good agreement with the results reported in References [70,71].
From the above presented results, it can be clearly noticed that the grating parameters played a significant role in the light absorption properties of the nanostructures. In addition, with the increment of incident angle, the reflection of p-polarised light decreased until it reached the minimum reflection level at an angle of 75 • before it started to rise again. However, the reflection of s-polarised light always increased for any angle of incidence. The light reflection of un-polarised remained at a constant stage from the beginning 0 • to 60 • and then increased exponentially afterwards as observed and explained in detail in our previously published article [72]. , and absorption (c) spectra for a trapezoidal-shaped nano-grating structure. The aspect ratio for the trapezoidal structure was 0.5. Figure 7a,b show the light reflection and transmission spectra for rectangular-shaped nano-gratings with the nano-grating heights ranging from 100 nm to 400 nm. The simulation results confirmed that the light reflection reduced with increasing the height and reached saturation around 200~250 nm. The reflection loss was minimum when the nano-grating height was ~200 nm. The light absorption curves for the rectangular-shaped nano-grating structures, for different grating heights from 100 nm to 400 nm, are shown in Figure 7c. This structure also represented the saturation of absorbed light around 250 nm~300 nm, and the capacity of light absorption decreased gradually afterwards, with decreasing nano-grating heights. The simulation results presented in this paper are in good agreement with the results reported in References [70,71].   , and absorption (c) spectra for a trapezoidal-shaped nano-grating structure. The aspect ratio for the trapezoidal structure was 0.5. Figure 7a,b show the light reflection and transmission spectra for rectangular-shaped nano-gratings with the nano-grating heights ranging from 100 nm to 400 nm. The simulation results confirmed that the light reflection reduced with increasing the height and reached saturation around 200~250 nm. The reflection loss was minimum when the nano-grating height was ~200 nm. The light absorption curves for the rectangular-shaped nano-grating structures, for different grating heights from 100 nm to 400 nm, are shown in Figure 7c. This structure also represented the saturation of absorbed light around 250 nm~300 nm, and the capacity of light absorption decreased gradually afterwards, with decreasing nano-grating heights. The simulation results presented in this paper are in good agreement with the results reported in References [70,71].

Conclusions
We have demonstrated the design, simulation, and analysis results of the light capturing properties of nano-gratings with different shapes and geometries. The optimised nano-structures, to be applied on top of the GaAs solar cells, showed the best optical properties (i.e., light transmission, reflection, and absorption), and enhanced the light absorption capacity of solar cells for the improvement of conversion efficiency. It is evident from the simulation results that triangular-shaped nano-grating structures can absorb more light into the GaAs substrate compared with other types of nano-grating shapes. The reason is that a series of consecutive reflections occur in the grooves (i.e., edges) of the inclined triangular walls, and more energy localisation happens due to the existence of sharp edges. Moreover, using antireflective layer properties leads to several-step changes in the refractive indices of the grating geometry. These simulation results confirmed that the use of nano-grating structures enables up to 27% higher light absorption capacity than conventional solar cells, and thus can increase the conversion efficiency of GaAs solar cells as expected [73]. Based on the achieved simulated results, it can be concluded that the reduction of light reflection losses will significantly increase the conversion efficiency of GaAs solar cells.