## 4 Electrical Modeling Results
### Electrical Modeling Procedure
For reference, reflectance spectrum and J–V curves are also calculated in the planar CIGS solar cell (**a**) without and (**b**) with the inclusion of the two front encapsulation layers. When the AM 1.5 sunlight is normally incident (\(\theta_{0}=0^{\circ}\)) in Figure 10a, the reflectance of the surface-textured CIGS solar cell without the front encapsulation layers has a very small value of less than 5% in nearly all the wavelength ranges. This results from the significant reduction of reflectance caused by light scattering effect at the surface-textured interface between the air and the AZO TCO. On the other hand, the reflectance of the surface-textured CIGS solar cell with the front encapsulation layers, which is determined by the incoherent multiple optical reflections as shown in Figure 8, is greater than that of the surface-textured CIGS solar cell without the front encapsulation layers. As the incidence angle of sunlight increases from \(\theta_{0}=0^{\circ}\), the degree of increase in reflectance of the surface-textured CIGS solar cell without the front encapsulation layers is relatively higher than that of the surface-textured CIGS solar cell with the front encapsulation layers. Thus, when the incidence angle of the AM 1.5 sunlight is \(\theta_{0}=60^{\circ}\) in Figure 10d, the reflectance of the surface-textured CIGS solar cell without the front encapsulation layers is either lower than or higher than that of the surface-textured CIGS solar cell with the front encapsulation layers in reference to the wavelength of 690 nm. Figure 11 shows the calculated J-V curves of four different device structures when the incidence angles of the AM 1.5 sunlight are \(0^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\). The corresponding values of \(\mathrm{J_{SC}}\) are summarized in \[J_{p}(\overrightarrow{r})=-q\mu_{p}p(\overrightarrow{r})\
abla V( \overrightarrow{r})-qD_{p}\
abla p(\overrightarrow{r}), \tag{20}\]2 In the case of surface-textured CIGS solar cells, optical calculation results are averaged over three different arbitrarily-textured surfaces at each RMS roughness to simulate CIGS solar cells with random surface-textured. This averaging procedure for the surface-textured CIGS solar cells can cause the deviation of the calculation results of \(\mathrm{J_{SC}}\) in \[J_{p}(\overrightarrow{r})=-q\mu_{p}p(\overrightarrow{r})\
abla V( \overrightarrow{r})-qD_{p}\
abla p(\overrightarrow{r}), \tag{20}\]3 The calculated standard deviations of \(\mathrm{J_{SC}}\) for the surface-textured CIGS solar cell without the front encapsulation layer are 0.18, 0.23, 0.22, and 0.34 at the incidence angles of \(0^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\), respectively. In the case of the surface-textured CIGS solar cell with the front encapsulation layer, the calculated standard deviations of \(\mathrm{J_{SC}}\) are 0.04, 0.08, 0.08, and 0.06 at the incidence angles of \(0^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\), respectively. Because of the larger refractive-index difference between the air and the TCO, the standard deviation of \(\mathrm{J_{SC}}\) is speculated to be greater for the surface-textured CIGS solar cell without front encapsulation layer. According to the calculated standard deviations for the surface-textured CIGS solar cells, all the calculation results of \(\mathrm{J_{SC}}\) are speculated to be within the error range. The surface-textured CIGS solar cells have a larger value of \(\mathrm{J_{SC}}\) than the planar CIGS solar cells due to the reflectance reduction and absorption enhancement caused by the scattering effect of the surface-textured structure. It is noticeable that the improvement percentage of \(\mathrm{J_{SC}}\) in the surface-textured CIGS solar cell over the planar CIGS solar cell is different whether the front incoherent encapsulation layers are included or not.