Design Multilayer Antireflection Coatings for Terrestrial Solar Cells

In order to analyze the influence of methods to design antireflection coatings (ARCs) on reflectivity of broadband solar cells, we provide detailed analyses about the ARC coupled with a window layer and the refractive index dispersion effect of each layer. By multidimensional matrix data simulation, two methods were employed to measure the composite reflection of a SiO2/ZnS double-layer ARC within the spectral ranges of 300–870 nm (dual junction) and 300–1850 nm (triple junction) under AM1.5 solar radiation. A comparison study, between the results obtained from the commonly used weighted average reflectance method (WAR) and that from the introduced effective average reflectance method (EAR), shows that the optimization of ARC by EAR method is convenient and feasible.


Introduction
Reflective loss of the incident light on the device surface is an important factor that affects efficiency of solar cell (SC). Design of antireflection structure has become a key factor in SC fabrication [1][2][3][4][5][6][7]. For III-V tandem SCs, a proper group of transparent materials are deposited on the SC surface, leading to the formation of antireflection coatings (ARCs) [7,8]. Consequently, the reflective loss of the incident lights would be minimized and the SCs work in a spectral range with higher efficiency. Therefore, broadband ARCs are essential for SCs operating at a broad spectrum.
Generally, there are various types of broadband ARC. For instance, flat multilayer ARCs can be double, triple, or quadruple layer. Many studies have shown that the performance of a single layer coating is not satisfying due to its narrow working spectral range. Double-, triple-, or even multiple-layer ARCs [7,[9][10][11] have better performance when referring to broadband SCs. Double-layer ARCs are commonly used because of their simple fabrication process and low cost. In this paper, the principle and method of antireflective films were introduced. A multidimensional matrix for the refractive index dispersion effect of each layer was used to simulate the reflectivity of several optical film systems. An effective average reflectance method (EAR) simplified from the commonly used weighted average reflectance method (WAR) was also utilized to design ARCs. The optimizations of ARCs in the dual-and triplejunction SCs by two methods were compared and analyzed. Accordingly, it demonstrates that optimizing ARC by minimizing is more convenient under the AM1.5 conditions. The models for optimization of multilayer ARC are presented in the following section, and their differences from a typical double-layer ARC are discussed in detail thereafter.

Methodology
The reflectivity at normal incidence of a SiO 2 /ZnS doublelayer antireflection coating (ARC) on an Al 0.5 In 0.5 P window layer is typically modeled in front of a Ga 0.5 In 0.5 P top cell. This approach is based on previously measured optical parameters for materials such as Al 0.5 In 0.5 P and Ga 0.5 In 0.5 P [12], as well as others [12][13][14] used as ARCs. The optical parameters of any composition of ARC are generally determined by cubic interpolation. We adopted the transfermatrix method to model the reflectance of the system, as this approach can be used to analyze multilayer films of varying thickness, refractive indices ( ), and extinction coefficients ( ) on a substrate. Optical interference matrix is an effective way to calculate reflectivity of film. To allow the situation that the incident angle of light is zero degree, considering the optical thin film system of layers prepared on the substrate as shown in Figure 1, is the refractive index and is the extinction coefficient, is the thickness in each layer, respectively, and 0 is refractive index of air ( 0 = 1). According to the refractive index and thickness of each layer, interference matrix of each layer can be determined. A characteristic matrix formulation of the film system is obtained by multiplying interference matrix of each layer [15]: where is the effective optical thickness of the layer at a given wavelength. The 2 is equal to the phase difference of two adjacent coherent light beams. = / is the optical admittance. The reflectivity of the whole film system is expressed as The solar spectrum spans a broad range of wavelengths. To enable more incident light to enter the SC, the internal quantum efficiency of the material and the sun's spectral characteristics should all be considered during the design of ARCs. The weighted average reflectivity within the entire spectrum can be calculated by the incident photon flux ( ) [16], the internal quantum efficiency (IQE) of the SC ( ) [17,18], and the reflectivity of monochromatic light ( ) [19]: (4)

Results and Discussion
In this section, we will discuss the minimization results obtained for the weighted average reflectance and effective average reflectance of the SiO 2 /ZnS double-layer structure on double-and triple-junction SCs under AM1.5 conditions. Figures 2 and 3 depict the optimal parameters of the SiO 2 /ZnS ARC for the Ga 0.5 In 0.5 P/GaAs double-junction SC under AM1.5 conditions. The reflectivity curves of SiO 2 /ZnS films optimized by and are shown in Figure 4. The SiO 2 /ZnS ARC parameters for the double-junction SC optimized by different methods are summarized in Table 1.

Dual Junction Solar Cell (300-870 nm). The fourdimensional images shown in
Those optimized by and exhibited minimal differences (see in Table 1), with the change in thickness values being less than 2 nm and the reflectivities in the spectral range of 400-700 nm remaining almost unchanged, that these reflectivities are the lowest where the solar photon flux is mainly distributed (see Figure 4). These results indicated that optimizing the ARC by minimizing the effective average reflectance for double-junction SC is feasible. (300-1850 nm). The fourdimensional images shown in Figures 5 and 6 depict  the optimal parameters of the SiO 2 /ZnS ARC for the Ga 0.5 In 0.5 P/GaAs/Ge triple-junction SC under AM1.5 conditions. The reflectivity curves of SiO 2 /ZnS films optimized by and are shown in Figure 7. The SiO 2 /ZnS ARC parameters for the triple-junction SC optimized by different methods are summarized in Table 2.  Those optimized by WAR and EAR methods also exhibited minimal differences in triple junction SC (see in Table 2), with the change in thickness values being less than 2 nm and the reflectivities in the spectral range of 400-700 nm remaining almost unchanged. The reflectivities are properly the lowest where the solar photon flux is mainly distributed (see Figure 7). These results indicated that optimizing the ARC by minimizing the effective average reflectance for double-junction SC is feasible.

Summary
To summarize, this study represents the theoretical optimization of the SiO 2 /ZnS double-layer ARC on the Al 0.5 In 0.5 P window layer for double-and triple-junction SCs under AM1.5 condition. It demonstrated that there are no considerable differences in the final optimal ARC parameters by WAR method and EAR method. For the double-junction SC, the changes in ARC thickness and average reflectivity were determined to be less than 2 nm and 0.07%, respectively. On the other hand, for the triple-junction SC, the corresponding values obtained were less than 6 nm and 0.76%, respectively. These slight changes in the parameters are acceptable. Therefore, optimizing ARCs by minimizing the introduced, instead of , as is commonly used, is thus a viable technique under AM1.5 condition.