# Broadening of Light Coupling to Waveguide Modes in Solar Cells by Disordered Grating Textures
## 3 Results and Discussion
### Impact of Disorder in Solar Cells  
In order to evaluate the impact of the disordered grating textures on the broadband performance of the a-Si:H solar cell, we simulated the EQE in the spectral range from 635 nm to 780 nm with a spectral resolution of 2 nm. For shorter wavelengths, the absorption coefficient of a-Si:H is too high for the formation of waveguide modes; for longer wavelengths, the absorption coefficient is too low to contribute significantly to the photocurrent generation at the given cell thickness. The results are shown in Figure 5. Figure 5a,b illustrate the broadening of the spectral resonances in the EQE due to the position disorder and radius disorder, respectively. In both illustrations, the black line corresponds to the perfect periodic case, which is characterized by distinct maxima in the EQE which are related to the resonant light coupling of incident light to waveguide modes in the absorber layer of the solar cell. The EQEs for the implementation of a moderate disorder into the grating textures are shown as red lines. These curves still show some resonant behavior, but with strongly reduced peak heights which are spectrally much broader. The blue curves depict the situation for a high degree of disorder. Resonant behaviors are no longer visible and the shape of the curves is smooth. Figure 4: Top view images of the frontside texture (**a–c**), backside texture (**d–f**), and local layer thickness (**g–i**) for the perfect periodic grating and the gratings with position and radius disorders. Obviously both physical effects, the less well-defined wave vector transfer in the case of the position disorder as well as the less well-defined waveguide mode in the case of the radius disorder lead to the similar effect of a smearing out of the resonant behavior of light coupling of incident light to guided modes in the absorber layer of the solar cell. Nevertheless, the two ways of applying disorder into the grating textures show significant differences. In the case of the position disorder (Figure 5a), the EQE is reduced at the spectral positions of the waveguide modes (e.g., at \(\lambda\)-720 nm) but reveal an overall improved EQE off of these spectral resonance positions (e.g., at 700 nm \(<\lambda<\) 715 nm or 725 nm \(<\lambda<\) 750 nm). This already suggests an overall improvement of photocurrent generation due to the implementation of position disorder into the grating texture. In contrast, the EQE curves in the case of the grating textures with radius disorder show spectral regions where the EQE is improved, but also other regions with a reduced response (e.g., at 670 nm \(<\lambda<\) 690 nm). In order to quantify the impact of the different ways of disorder on the solar cell performance in the broad spectral range, the photocurrent is determined for each structure and the results are compared to each other. Therefore, the simulated EQE curves are weighted by the solar irradiance and spectrally integrated to obtain the short-circuit current density (J\({}_{\text{SC}}\)) of the solar cells generated in the spectral region from 635 nm to 780 nm. The results are plotted in Figure 6 as a function of the respective disorder parameter. We found that an increase of position disorder monotonically enhances the short-circuit current density (blue solid line). At larger disorder, J\({}_{\text{SC}}\) of the solar cell saturates. The radius disorder (red dashed line) shows a different trend. For smaller disorder parameters up to 45 nm, the J\({}_{\text{SC}}\) increases. Afterwards, the short-circuit current density decreases while still surpassing the level of the well-ordered periodic texture. Both investigated ways of introducing disorder into the grating structure lead to an improvement of J\({}_{\text{SC}}\) of the solar cell as long as the strength of disorder is moderate. With a higher degree of disorder, the impact on the solar cell performance varies for the different ways of disorder. The J\({}_{\text{SC}}\) of the solar cells with position disorder in the grating texture saturates.