# Opal-Like Photonic Structuring of Perovskite Solar Cells Using a Genetic Algorithm Approach
## 2 Design of the Perovskite Solar Cell  
The combination of PSCs under investigation is based on representative PV devices described in the literature [39] and is shown in Figure 1.  
The incident (emergence) medium is composed of a semi-infinite, non-dispersive glass (air) slab with a refractive index \(n_{i}\left(n_{s}\right)\) of 1.5 (1). The first layer of the photonic structure consists of a uniform transparent conducting electrode layer made of fluorine-doped tin oxide (_FTO_), with its thickness denoted as \(t_{FTO}\). This thickness is the first variable for the GA optimization and varies from 50 to 800 nm. A numerical resolution of 10 nm is chosen for all parameters. A uniform hole blocking layer made of _TiO\({}_{2}\)_ is placed above the photo-active hybrid perovskite layer. Its thickness is fixed to 40 nm according to optimized results from the literature [33; 40; 41; 42]. Both refractive indices of the _FTO_ and _TiO\({}_{2}\)_ layers are taken from [42]. Importantly, the optical bandgap of _TiO\({}_{2}\)_ is 385 nm, implying that this layer slightly absorbs incident light in the following simulations, introducing some additional parasitic absorption, namely absorption occurring outside of the photo-active layer, in the short wavelength part of the spectrum (310-385 nm). The third layer is a hybrid photo-active layer made of a uniform homogeneous layer and of spheres of methylammonium lead triiodide (_MAPbI\({}_{3}\)_) perovskite arranged according to a face-centered cubic (_fcc_) close-packed structure (filling fraction of 0.74) with _ABC_ stacking. The spheres are integrated within a mesoporous _TiO\({}_{2}\)_ host matrix acting as an electron-collecting electrode. At the structured perovskite-TiO\({}_{2}\) layer interface, the spheres might be non-entire. This choice adds two advantages to the structure. It first confers more photonic flexibility for the light trapping at the interface (i.e., it introduces a new parameter that can be used during the GA optimization). Secondly, this approach involving potentially non-entire spheres formalizes a less ideal case, better reproducing the experimental reality than with entire spheres, the latter being the ideal case limit described in our previous work [33]. Therefore, the two important parameters for the structured part of the photo-active layer are (i) the radius \(R\) of the spheres and (ii) the thickness \(t_{struc}\) of the structured perovskite layer. The radius of the spheres can be tuned by selecting appropriate polystyrene beads that act as structuring agents during the synthesis of the inverse opal _TiO\({}_{2}\)_ porous films. In the following, \(R\) can vary between 50 nm and 1100 nm. The thickness \(t_{struc}\) can be controlled by the quantity of perovskite being infiltrated inside the spherical pores left after calcination of the _TiO\({}_{2}\)_ precursor solution. The thickness \(t_{struc}\) will vary between 50 nm and 2200 nm. These potentially non-entire spheres represent the opal-like subunits used in the photonic structuring strategy applied here. The presence of a uniform perovskite layer underneath the structured part of the photo-active layer confers a hybrid character to the photo-active layer (a mix of unstructured and structured layers), differing from the previous structures investigated to date in the literature, and consequently differing from our previous study [33]. This layer is often observed experimentally when the TiO\({}_{2}\) porous matrix is overfilled by perovskite during the infiltration process. The thickness \(t_{uni}\) of this uniform layer will vary between 0 (no layer) and 100 nm. To complete the design of the PSC, a hole transporting (HT) layer made of 2,2',7,7'-Tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9'-spirobifluororene or \"spiro-OMeTAD\" (C\({}_{81}\)H\({}_{68}\)N\({}_{4}\)O\({}_{8}\)) is placed between the hybrid photo-active layer and a gold counter-electrode. The thickness \(t_{spiro}\) of the HT layer is our last parameter, varying between 50 and 800 nm.