## 4 Electrical Modeling Results  
### Electrical Modeling Procedure  
The J-V characteristics of the CIGS solar cell are calculated based on the 2D numerical solution of the drift-diffusion model, which is expressed as [24]  
\[J_{n}(\overrightarrow{r})=-q\mu_{n}n(\overrightarrow{r})\
abla V( \overrightarrow{r})+qD_{n}\
abla n(\overrightarrow{r}), \tag{19}\]  
\[J_{p}(\overrightarrow{r})=-q\mu_{p}p(\overrightarrow{r})\
abla V( \overrightarrow{r})-qD_{p}\
abla p(\overrightarrow{r}), \tag{20}\]  
\[\epsilon_{0}\
abla\cdot\left[\epsilon_{r}\
abla V(\overrightarrow{r})\right] =q[n(\overrightarrow{r})-p(\overrightarrow{r})+N_{A}^{-}(\overrightarrow{r })-N_{D}^{+}(\overrightarrow{r})], \tag{21}\]  
\[(1/q)\
abla\cdot J_{n}(\overrightarrow{r})=-\left[G(\overrightarrow{r})-R( \overrightarrow{r})\right], \tag{22}\]  
\[(1/q)\
abla\cdot J_{p}(\overrightarrow{r})=\left[G(\overrightarrow{r})-R( \overrightarrow{r})\right], \tag{23}\]  
where \(q\) is the basic electric charge. In the current equation of Equations (19) and (20), \(J_{n}(\overrightarrow{r})\) and \(J_{p}(\overrightarrow{r})\) are electron and hole current densities when \(\mu_{n(p)}\) and \(D_{n(p)}\) represent electron (hole) mobility and diffusion coefficient, respectively. The terms \(n(\overrightarrow{r})\), \(p(\overrightarrow{r})\), and \(V(\overrightarrow{r})\) indicate the electron concentration, hole concentration, and electric potential, which are related through the Poisson equation of Equation (21) when \(\varepsilon_{r}\), \(N_{A}^{-}(\overrightarrow{r})\), and \(N_{D}^{+}(\overrightarrow{r})\) are the dielectric constant, acceptor concentration, and donor concentration. In the continuity  
Figure 8: Calculated ADETAM-applied reflectance spectra of the surface-textured CIGS solar cell at different degrees of the RMS surface roughness when the incidence angle of the AM 1.5 sunlight is \(\theta_{0}=\) (**a**) 0\({}^{\circ}\), (**b**) 30\({}^{\circ}\), (**c**) 45\({}^{\circ}\), and (**d**) 60\({}^{\circ}\). The incidence-angle-dependent reflectance of the incoherent multiple optical reflections calculated by Equation (18) is well matched with the minimum reflectance values of the surface-textured CIGS solar cell with \(\sigma_{\text{RMS}}=100\) nm. equation of Equations (22) and (23), \(G(\overrightarrow{r})\) represents the generation rate of the electron-hole pair and can be obtained by  
\[G(\overrightarrow{r})=\int S(\lambda)\frac{\left(\overline{Q}^{i}(\lambda, \overrightarrow{r})+\overline{Q}^{p}(\lambda,\overrightarrow{r})\right)/2}{ hc/\lambda}d\lambda, \tag{24}\]  
where \(h\) is the Plank constant, and \(c\) is the speed of light in a free space. The ADETAM-applied spatial distribution of light absorption for s(p)-polarized light is \(\overline{Q}^{s(p)}(\lambda,\overrightarrow{r})\), whose values are averaged to represent unpolarized light. Finally, \(R(\overrightarrow{r})\) represents the recombination rate of the electron-hole pair and is given by  
\[R(\overrightarrow{r})=R_{SRH}(\overrightarrow{r})+R_{rad}(\overrightarrow {r}), \tag{25}\]  
where \(R_{SRH}(\overrightarrow{r})\) and \(R_{rad}(\overrightarrow{r})\) are the non-radiative Shockley-Read-Hall (SRH) recombination and radiative recombination rates [33]. The 2D drift-diffusion model, shown in Equations (19)-(25), are numerically solved through the semiconductor module of the COMSOL Multiphysics [32]. In the 2D simulation domains of the planar CIGS solar cell in Figure 2a and surface-textured CIGS solar cell in Figure 6a, both the top anode terminal of the AZO/ZnS interface and the bottom cathode terminal of the Mo/CIGS interface are assumed to be ideal Schottky contacts. The J-V characteristics are calculated at only the regions containing the ZnS and CIGS layer. To minimize the error of a mismatch, the electrical modeling is performed under the same mesh configuration as the optical modeling. The periodic conditions are applied at the leftmost and rightmost boundaries of the simulation domain. The simulation parameters used in the electrical modeling are obtained in [33].