# Opal-Like Photonic Structuring of Perovskite Solar Cells Using a Genetic Algorithm Approach
## 4 Results
### Robustness of the Optimum  
It is interesting to quantify the robustness of the optimum provided by the GA algorithm with respect to potential experimental deviations from ideality. We present in Figures 4 and 5 two 2D maps showing the linear interpolations of the iQE as a function of the radius of the perovskite spheres, \(R\); the thickness of the structured perovskite layer, \(t_{struc}\); and the thickness of the perovskite uniform layer, \(t_{uni}\). Those are the three main parameters responsible for useful absorption inside the PSC. The optimal values (Table 2) are labeled with a red star. The blue dots indicate the parameters where the iQE has been evaluated exactly. As we can observe, the GA has explored a lot of combinations around the optimum, indicating the reliability of the solution. The \(R-t_{struc}\) 2D map (Figure 4) shows two distinct 200 nm \(\times\) 200 nm 2D boxes. The black box centered around the optimum determined by the GA provides an average iQE of 97.0% (average of interpolated fitness values in this 2D plane), thus \(\Delta=1.1\%\), showing a reasonably robust optimum. The blue box refers to the sweet spot. It can be seen that the sweet spot does not overlap with the maximum established by the GA. The averaged iQE inside the sweet spot is 97.3%, providing a \(\delta\) of 0.9%. Since \(\delta<\Delta\), it confirms the interest of the sweet spot for the \(R-t_{struc}\) parameters.  
Figure 3: Absorptance (yellow) and reflectance (blue) spectra for the optimal combination, providing an iQE of 98.1% (solid lines) for the PSCs. Comparison is made with an unstructured PSC containing the same volume of absorbing material (dashed lines).  
Figure 4: A 2D map of the iQE as a function of the radius of the perovskite spheres \(R\) and the thickness of the structured perovskite layer \(t_{struc}\), two of the main parameters regarding absorption in the PSCs. Blue dots indicate evaluation of the iQE made by the GA, the red star indicates the optimal combination, the blue box indicates the sweet spot, and the black box indicates the 200 nm \(\times\) 200 nm box around the optimal combination.  
Figure 5: A 2D map of the iQE as a function of the thickness of the homogeneous perovskite layer \(t_{uni}\) and the thickness of the structured perovskite layer \(t_{struc}\), two of the main parameters regarding absorption in the PSCs. Blue dots indicate evaluation of the iQE made by the GA, the red star indicates the optimal combination, the blue box indicates the sweet spot, and the black box indicates a 40 nm \((t_{uni})\times\) 200 nm \((t_{struc})\) box around the optimal combination.  
Regarding the \(t_{uni}-t_{struc}\) 2D map (Figure 5), a reasonably good overlap between the sweet spot and the 2D box centered around the optimum can be observed. The 2D boxes measure 40 nm (\(t_{uni}\)) by 200 nm (\(t_{struc}\)). We find that \(\Delta=0.4\%\) and \(\delta=0.3\%\). Even if \(\delta<\Delta\), the difference is smaller and there is no reason to choose the parameters from the sweet spot over the optimum ones.  
One can state from the above results that the optimum found by the GA optimization process is quite robust regarding any imperfection that might occur during the experimental fabrication process, regarding the parameters that are the most sensitive to the iQE.