## 2 Optics of Microcrystalline Silicon Solar Cells  
To describe the wave propagation in silicon thin-film solar cells, simple geometric or wave optics is insufficient. Instead, it is necessary to rigorously solve [PERSON]'s equations. Currently, there are a number of methods being utilized such as the finite-difference time-domain (FDTD) method [21], finite integration method (FIM) [22] or Rigorous Coupled Wave Analysis (RCWA) [23] capable of simulating near- and far-field wave propagation in such devices. For this study, a FDTD simulation tool is used to investigate the wave propagation within solar cell structures [24]. The schematic cross-sections of microcrystalline silicon (\(\upmu\)C-Si:H) solar cells in superstrate configuration are depicted in Figure 1. A solar cell on a flat substrate is shown in Figure 1a. Cross-sections of solar cells with textured contacts and absorber layer are shown in Figure 1b,c, respectively. The cross section in Figure 1b,c shows a slice through the center of a 3D unit cell. All three solar cell structures follow the same basic layer sequence with: a 500 nm thick sputtered aluminum doped zinc oxide (ZnO:Al) front contact, followed by a \(\upmu\)C-Si:H _p-i-n_ diode with a total thickness of 1000 nm, a back reflector consisting of 80 nm thick ZnO:Al, and a perfect electrical conductor (PEC, 100% reflection) terminating the stack. The layer sequence used for the simulations is consistent with structures used in the literature [4; 6]. The thickness of the ZnO:Al front contact layer is consistent with reference solar cells prepared on flat substrates [4; 6]. The thickness of the p-layer of _p-i-n_ diode is assumed to be 30 nm, while the _n_-layer of the _p-i-n_ diode has a thickness of 10 nm. In order to realize a solar cell with textured absorber, the _p-i-n_ diode is patterned, while, in the case of a solar cell with textured contacts, only the front contact is textured. Subsequently, the _p-i-n_ layer stack and back contact of the solar cell with textured contacts are formed on the front contact. The morphology of the _p-i-n_ layer stack and back contact follows the front contact morphology. Hence, all layers of the solar cell are textured. However, in the following the structure is named solar cell with textured contact layers to point out that only the front contact layer is intentionally textured during the fabrication process. The subsequently formed _p-i-n_ layer stack is unintentionally textured. The texturing of the _p-i-n_ layer stack is the consequence of preparing the layers on a textured substrate. The optical constants of the \(\upmu\)C-Si:H material and the ZnO:Al film are adapted from the literature [4]. As the first step of the FDTD optical simulations, the electrical field distribution is calculated for a unit solar cell structure assuming normal incidence light with an electric field amplitude of 1 V/m. Figure 1: Cross-section of silicon thin-film solar cells with: (**a**) flat substrate; (**b**) textured absorber; and (**c**) textured contact layers. Based on the electric field distribution, the time-averaged power loss (\(Q(x\),\(y\),\(z\))) is determined within the solar cell via the equation:  
\[Q(x,y,z)=\frac{1}{2}ce_{0}na|E(x,y,z)|^{2}, \tag{1}\]  
where \(c\) is the speed of light in free space, \(\varepsilon_{0}\) is the permittivity of free space, \(\alpha\) is the absorption coefficient of the material at the given position, \(n\) is the real part of the complex refractive index, and \(E(x\),\(y\),\(z\)) is the electric field. The absorption coefficient is calculated by \(\alpha(\lambda)=4\pi k/\lambda\), where \(\lambda\) is the wavelength and \(k\) is the imaginary part of the complex refractive index. The absorption of light by the individual layer of the solar cell is defined as the ratio of the power absorbed by the layer with respect to the total power incident, \(P_{opt}\), on the unit cell.