## 2 Optoelectronic Modeling Methods  
### Optical Modeling  
Figure 1 shows a schematic diagram of the multilayer structure of the CIGS solar cell used in this study [17,19]. It comprises a cover glass (3 mm) at the top, aluminum-doped zinc oxide (AZO) (50 nm) as a TCO, zinc sulfide (ZnS) (10 nm) as an n-doped layer, CIGS (2 um) as a p-doped layer and molybdenum (Mo) (400 nm) as a bottom contact layer. The bottom glass substrate is omitted because it does not affect the optical and electrical characteristics of the CIGS solar cell. Sunlight is assumed to have a spectral irradiance of air mass (AM) 1.5 sunlight \(S(\lambda)\) with a total power of \(S_{0}=\) 100 mW/cm\({}^{2}\). Sunlight is assumed to be normally incident from the air into the CIGS solar cell, which can be optically modeled as a mixed incoherent-coherent multilayer structure. The 3-mm cover glass, the thickness of which is larger than the coherence length of sunlight (-0.6 um), is considered optically incoherent. In optical modeling based on the ETAM, the thickness of the transparent incoherent layer can be converted into the corresponding optical phase change, which has a period of 2\(\pi\). Thus, the thickness of the transparent cover glass used in the simulation does not require an actual thickness of 3 mm [18,19]. To reduce the computation time, we use a 1-um-thick initial cover glass layer in addition to the EPL, the role of which is to efficiently model a random phase change of light in the incoherent layer through a set of equispaced phase thicknesses in the EPL [18]. The remaining four layers were treated as coherent layers. Nearly all incident lights were absorbed around the interface between the ZnS and CIGS layers and there is no optical interference effect on the light absorption characteristics of the CIGS layer, which will be explained later. Thus, the CIGS layer can be treated as optically coherent although its 2-um thickness is greater than the coherence length of sunlight. In the optical modeling, we assume that all materials used in the CIGS solar cell were non-magnetic, linear, isotropic and homogeneous media with an instantaneous response. If \(\overrightarrow{r}=x\hat{a}_{x}+z\hat{a}_{z}\) indicates the position on the x-z plane in Figure 1, the wave equation can be written as  
Figure 1: Schematic diagram of multilayer structure of the Cu(In,Ga)Se\({}_{2}\) (CIGS) solar cell used in this study. The 3-mm cover glass, the thickness of which is larger than the coherence length of sunlight (-0.6 μm), is considered as incoherent, and the remaining layers are modeled as coherent. Because the 3-mm cover glass has no absorption, the incoherent cover glass can be modeled as a 1-μm initial cover glass layer plus an equispaced phase layers (EPLs) whose thickness \(t_{b}\) is determined based on Equation (17) when the equispaced thickness averaging method (ETAM) is applied to calculate the effect of the incoherent front glass layer in the simulation. \[\
abla\times\left[\
abla\times\overrightarrow{E}(\overrightarrow{r},\lambda) \right]-k_{0}^{2}\overrightarrow{n}^{2}\overrightarrow{E}(\overrightarrow{r},\lambda)=0, \tag{1}\]  
where \(\overrightarrow{E}(\overrightarrow{r},\lambda)\) is the electric field amplitude at a wavelength of \(\lambda\), and \(k_{0}=2\pi/\lambda\) is the wave number of the free space. The complex refractive index of the materials is expressed as \(\overrightarrow{n}=\overrightarrow{n}-j\kappa\), where \(\overrightarrow{n}\) and \(\kappa\) were the refractive index and extinction coefficient, respectively. If \(t_{b}\) represents the equispaced phase thickness of the EPL in Figure 1, the numerical solution of the wave equation in Equation (1) depends on the value of \(t_{b}\).