# Opal-Like Photonic Structuring of Perovskite Solar Cells Using a Genetic Algorithm Approach
## 4 Results  
### Optimum  
We present here the results of the GA optimization process. Figure 2 shows the best iQE and the mean iQE in the population as a function of the number of generations. A reasonably fast progression of the algorithm is noticed already after 6 generations. The global optimum is found at generation 34 (genetic similarity \(s\) of 84.8%), with a related iQE equal to 98.1%. All further generations do not provide a better iQE up to 84 generations. The global optimum found at generation 34 (red cross) corresponds then to the best combination of the parameters and is kept for all further generations. The value of 98.1% gives an idea of the averaged absorptance over the 310-800 nm wavelength range. The parameters for this global optimum are summarized in Table 2 below.  
The corresponding structure encompasses four entire spheres and part of a fifth sphere on top of the structured perovskite layer. It can be noticed that the iQE is maximal for high values of \(t_{uni}\) (80 nm, where the maximal allowed value was 100 nm) and \(t_{struc}\) (2080 nm, where the maximal allowed value was 2200 nm). Logically, more absorption occurs inside the PSCs if more absorbing material is present.  
One can compare the difference between structured and unstructured PSCs by considering an equivalent layer of uniform perovskite with the parameters for the optimal iQE (\(t_{uni}=80\ nm\) and \(t_{struc}=2080\ nm\)). This equivalent thickness is given by \(t_{\alpha\eta}=t_{uni}+0.74\times t_{struc}=1620\ nm\). The corresponding iQE is 96.2%. The corresponding photonic enhancement factor, \(G_{phot}=(iQE(structured)-iQE(unstructured))/(iQE(structured)\times 100\), is equal to 2%. This confirms the positive impact on light absorption of structuring of the photo-active layer. A closer examination of the absorptance spectrum (Figure 3) reveals an enhanced absorptance just before the optical bandgap of perovskite. This was indeed the expected goal of structuring the photo-active layer. Quasi-guided modes are excited inside the perovskite spheres [33] and the GA optimization favors the spheres with the right radius, with the Fano resonance positioned close to the optical bandgap. It should be noted that the peaks present above 800 nm are related to parasitic absorption, and therefore are not directly useful for the production of electron-hole pairs without additional knowledge of the electrical  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Name** & **Optimum** \\  & **Value** \\ \hline Thickness of the transparent conducting electrode fluorine-doped tin oxide \(FTO\) layer \(t_{FTO}\) & 710 nm \\ Thickness of the uniform perovskite layer \(t_{uni}\) & 80 nm \\ Radius of the perovskite spheres \(R\) & 300 nm \\ Thickness of the structured perovskite layer \(t_{struc}\) & 2080 nm \\ Thickness of the hole transporting spiro–OMeTAD layer \(t_{spiro}\) & 240 nm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Optimum parameters provided by the GA optimization process.  
Figure 2: Convergence of the integrated quantum efficiency (iQE) as a function of the number of generations, showing the best (square) and the mean (circle) iQE in the population in the first 84 generations when optimizing the PSCs. The combination giving the optimal iQE is found after 34 generations (red cross). Between generation 34 and 84, no better solution is found by the GA. The parameters for the optimal combination are listed in Table 2.  
properties of excitons in perovskite. Parasitic absorption (in \(TiO_{2}\) for example) is always included in our calculations, and therefore the obtained results should be considered as an upper maximal value. It is interesting to note that the optimized thickness for the HT layer outputted by the GA optimization is close to the value present in the literature (\(t_{spiro}=240\) nm instead of 250 nm [(40; 41)]).