# Opal-Like Photonic Structuring of Perovskite Solar Cells Using a Genetic Algorithm Approach
## 1 Introduction
Nevertheless, methylammonium lead triiodide still exhibits a high photon penetration depth around its bandgap (around 800 nm [22]). It severely reduces the absorption in this wavelength range, and consequently the number of electron-hole pairs that are photo-generated. Therefore, the idea of applying photonic management strategies, which have been successfully demonstrated for Si solar cells, to PSCs came along recently [25; 26; 27; 28; 29; 30; 31; 32; 33]. Inverse opal perovskite films have previously been successfully prepared and [PERSON] et al. [27] demonstrated that an optimal radius of 200 nm results in a promising PCE of 11.7% compared to an island-like perovskite film of PCE equal to 5.6%. [PERSON] et al. achieved a PCE of 17.1% using 600 nm-thick inverse opal perovskite films (with the radius of the spheres being equal to 50 nm) [28], while [PERSON] et al. experimentally demonstrated that a 2D periodic array of holes inside a perovskite film was able to excite quasi-guided modes in thin film PSCs [31]. The latter photonic management strategy showed an improved PCE of 2% compared to planar structures. Recently, our team numerically investigated the positive impact of photonic structuring inside PSCs. Without a specific optimization scheme, we evidenced a maximal relative enhancement of 6.4% in the spectrally integrated absorbed photon flux, with the photo-active layer consisting of a monolayer of entire perovskite spheres (radius of the spheres being equal to 175 nm) instead of a homogeneous perovskite layer [33]. Additional layers of spheres increase the integrated quantum efficiency (iQE). For example, three layers of entire perovskite spheres arranged in a face-centered, cubic, closed-packed structure with \(ABC\) stacking allowed for an iQE of 96.7% over the 310-800 nm wavelength range. The 3D interconnected structure of inverse opals allows the excitation of quasi-guided modes within the active layer, which increases the photon lifetime inside the desired layer. Off the strength of those results, the main goal of this study is to further optimize the rational structure of PSCs to be closer to experimental reality by using a genetic algorithm (GA). The GA finds a global optimum or a high-quality solution within a multi-dimensional parameter space for a dedicated problem, such as light absorption [34; 35; 36]. This procedure enables the smart exploration of a larger range of parameters and is particularly relevant for the absorption inside the PSCs (e.g., the thicknesses of the different layers or the radius of the spheres). The GA approach is interesting, since it finds a global optimum without specifically testing each combination (their number increases exponentially with the number of parameters). The GA does not require the computation of gradients,In contrast with algorithms such as the (quasi-)Newton method or gradient descent, the GA is able to find the global optimum of a problem, while the former methods converge to the first local optimum encountered. In contrast with a standard simulated annealing algorithm, the GA enables a collective exploration of the parameter space, since a whole population actually contributes to this exploration. The GA can easily escape the local optima, since it requires only one individual to find a better place to attract the rest of the population. Compared to a GA based on a real number encoding of the parameters, a GA that relies on binary encoding, as in this work, will account for the precision required for these parameters in every operation. Instead of improving an unnecessarily large number of digits, a binary-encoded GA will keep exploring globally before converging to a solution with just the required precision [37; 38]. Combined with an intrinsic suitability for parallel computing, a binary-encoded GA is especially attractive for optical engineering problems. This approach allows us to provide a stable range of experimental parameters that will lead to robust EM absorption. Our manuscript is organized as follows.