# Broadening of Light Coupling to Waveguide Modes in Solar Cells by Disordered Grating Textures
## 3 Results and Discussion
### Local Layer Thickness  
It is difficult to quantify the impact of the interface structure of a wave guiding slab on the spectral width of the light coupling to the resonance mode as, without any interface structure, this  
Figure 2: (**a–c**) Representative topography images of the periodic grating texture, the texture with introduced position disorder and with radius disorder, respectively. (**d–f**) The corresponding images of the 2D-Fast Fourier transformation (FFT) applied to the textures shown in (**a–c**), respectively. light coupling is not possible at all. The situation becomes much more complex when looking for the impact of disorder within a grating coupler on the spectral width of the waveguide mode. On the one hand, the waveguide mode is already influenced in the case of the ordered grating structure. On the other hand, the disorder in the grating structure already influences the wave vector that is transferred to incident photons in a way that the resonance mode spectrally broadens. In the present study, the wave guiding slab is grown on top of a textured substrate, which means that the interfaces of the slab are corrugated. In particular, the growth of a-Si:H can be assumed to be isotropic, which leads to a modification of the backside texture as compared to the frontside texture [12]. Due to this isotropic growth, the thickness of the wave guiding layer fluctuates along the surface texture when the thickness is defined along the intentional growth direction. Since its thickness is a main parameter to determine the resonance condition of a wave guiding slab, the disorder in the local layer thickness behavior can be used to investigate the impact of the disorder on the quality of the wave guiding properties. Figure 3 shows the height profiles for the frontside texture (black lines), the backside texture (red lines) and the corresponding local layer thickness (red dashed lines), which is defined by the difference between the height profile at the backside and at the frontside. The results for the perfect periodic case are shown in Figure 3a, while those for a representation of a radius disorder introduced into the grating structure are shown in Figure 3b. Although the frontside textures of both structures (periodic and with radius disorder) look quite different from each other, the corresponding backside textures appear to be very similar. Small differences can only be obtained by a close look. This is a result of the isotropic growth of a-Si:H. As a consequence, the local layer thicknesses show significant differences depending on the applied disorder. In order to visualize this for the different investigated textures, top view images of the frontside texture, the backside texture, and the local layer thickness are illustrated in Figure 4 for the perfect periodic case and the structures with position disorder and radius disorder. As expected, the frontside textures (Figure 4a-c) reveal significant differences for the differently applied disorder. The backside textures (Figure 4d-f)) are more or less equalized for the perfect periodic case and the texture with radius disorder. Significant differences were only found for the texture with position disorder. This is a result of the isotropic growth of a-Si:H on top of the structured interface. Due to this growth behavior, the radius of the half-conically shaped nanostructures increases with the layer thickness. As long as the layer thickness reaches or exceeds half the distance between the nanostructures, the resulting radius is defined by the layer thickness rather than the original radius. Figure 3: **(a)** Height profile of the frontside (black) and backside (red) texture for the perfect periodic texture. The dashed blue line indicates the local thickness of the wave guiding slab along the line profile. **(b)** The same quantities are shown for a special representation of an introduced radius disorder into the grating structure. This has a strong impact on the local layer thickness, as can be seen in Figure 4g-i.