_applied sciences_  
_Article_  
**Dimensional Optimization of TiO\({}_{2}\) Nanodisk Photonic Crystals on Lead Iodide (MAPbI\({}_{3}\)) Perovskite Solar Cells by Using FDTD Simulations**  
**[PERSON] 1,*, [PERSON] 1**\({}^{\copyright}\)**, [PERSON] 2**\({}^{\copyright}\)**, [PERSON] 2, [PERSON] 1,3,  
**[PERSON] 1 and [PERSON]. [PERSON] 4**\({}^{\copyright}\)**  
Footnote 1: footnotemark:  
Footnote 2: footnotemark:  
Footnote 3: footnotemark:  
Footnote 4: footnotemark:  
Footnote 5: footnotemark:  
Footnote 6: footnotemark:  
Footnote 7: footnotemark:  
Footnote 8: footnotemark:  
Footnote 9: foot  
+++ ==WARNING: Truncated because of repetitions==
notemark:  
++  
known to maximize light absorption in a particular wavelength range because it has a slow photon effect that increases the interaction of photons and materials [12, 13]. PC also has a bandgap, or, specifically, a photonic bandgap (PBG), which is the gap between two adjacent photonic band structures. There are three types of PC based on their spatial arrangement, namely, one-dimensional, two-dimensional, and three-dimensional PC [14]. The higher the dimension, the better the optics enhancement quality. However, the highest dimension of PC (3D) is 1 \(\upmu\)m thick instead of in the range of sub-micrometer. Furthermore, it has a complex structure, so the fabrication is more complicated and requires better preparation technologies [15, 16].  
This study applies a 2D PC in the electron transporting layer (ETL). ETL is a perovskite-coated conductive layer that extracts electrons from the perovskite and carries them to the transparent electrode, resulting in charge recombination [17, 18]. The hole transport layer will do the same to the holes as well. Thus, the electron-hole charge recombination can be reduced by utilizing the slow photon effect.  
Various types of PC structures have been applied to PSC. [PERSON] et al. have demonstrated this by applying photonic crystals to organic solar cells [19]. There is an increase in light absorption and electrical properties, such as the short circuit current (\(J_{\mathrm{sc}}\)), fill factor, and open circuit potential (\(V_{\alpha\mathrm{c}}\)), compared to planar layers. [PERSON] et al. applied nanodisk photonic crystals to ETL and demonstrated greater absorption enhancement and current density than in ETL without photonic crystals [16]. By comparing several studies that applied photonic crystals on PSC to date, it is known that nanodisk photonic crystals with a two-dimensional hexagonal layout design by [PERSON] et al. produce the highest performance [16, 20, 21, 22, 23, 24, 25, 26, 27, 28]. This work has a similar focus to that of [PERSON]'s et al. study [5]; that is, to study the interface of absorber/ETL. The result shows that their structure provides better performance. The differences between both works are the material used as an absorber layer. [PERSON] et al. use mixed cations and halides perovskite, (Cs\({}_{\mathrm{x}}\)(MA\({}_{0.17}\)FA\({}_{0.83}\))(100-x)Pb(\({}_{0.83}\)Br\({}_{0.17}\))\({}_{3}\)), while [PERSON] et al. use MAPb\({}_{3}\)[5, 16]. Therefore, further study of nanodisk photonic crystals on lead iodide (MAPb\({}_{3}\)) is required to improve the PSC performances.  
This study modified the MAPb\({}_{3}\) PSC using nanodisk PC on titanium dioxide (TiO\({}_{2}\)) materials. The geometry of PC, including the lattice constant and radius, is optimized using the finite-difference time-domain (FDTD) method. This optimization was made based on the study of PBG dependence on the PC structure [29]. The PBG changed when the size of the photonic crystal was modified. Furthermore, in this study, variations of the lattice constant and radius of photonic crystal were made to find the optimum PBG. This optimum design can be seen by its optical performance. The optimized performance was determined based on their optical performance. Finally, this study was expected to prove the advantage of PC in the solar cell by providing the enhancement of PSC performance compared to a non-PC structure.