## 2 Materials and Methods  
In this study, the current density-voltage (_J_-_V_) plot, _V\({}_{\alpha}\), _J\({}_{\infty}\)_, fill factor (_FF_), and _PCE_ of the ITO/TiO\({}_{2}\)/MAPbI\({}_{3}\)/Cu\({}_{2}\)O/Au solar cell with MAPbI\({}_{3}\) as an absorber were calculated using the numerical simulation program SCAPS-1D [50; 51]. In the SCAPS-1D program, each output value is derived through Equations (1)-(5) [52; 53; 54].  
[PERSON]'s equation is commonly used for simulating semiconductor devices:  
\[\frac{d^{2}}{dx^{2}}\psi(x)=\frac{e}{\varepsilon_{0}\varepsilon_{r}}(p(x)-n(x) +N_{D}-N_{A}+\rho_{P}-\rho_{n}) \tag{1}\]  
Here, \(\psi\) is the electrostatic potential, \(e\) is the electrical charge, \(\varepsilon_{r}\) is the relative permittivity, \(\varepsilon_{0}\) is the vacuum permittivity, \(p\) and \(n\) are the hole and electron concentrations, \(N_{D}\) and \(N_{A}\) are the charged impurities of the donor and acceptor types, and \(\rho_{P}\) and \(\rho_{n}\) are the distributions of holes and electrons, respectively.  
The continuity equations for electrons and holes are:  
\[\frac{dj_{n}}{dx}=G-R \tag{2}\]  
\[\frac{dj_{p}}{dx}=G-R \tag{3}\]  
Here, \(j_{n}\) is the electron current density, \(j_{p}\) is the hole current density, \(G\) is the generation rate, and \(R\) is the recombination rate.  
\[J_{n}=D_{n}\frac{d_{n}}{dx}+\mu_{n}n\frac{d\varphi}{d_{x}} \tag{4}\]  
\[J_{p}=D_{p}\frac{d_{p}}{d_{x}}+\mu_{p}p\frac{d\varphi}{d_{x}} \tag{5}\]  
In the above drift-diffusion model, \(\mu_{n}\) is the mobility of electrons, \(\mu_{p}\) is the mobility of holes, \(D_{n}\) is the electron diffusion coefficient, and \(D_{p}\) is the hole diffusion coefficient. Figure 1a shows the basic structure of the PSC considered in this study: ITO/TiO\({}_{2}\)/MAPbI\({}_{3}\)/Cu\({}_{2}\)O/Au. ITO was used as the front contact, TiO\({}_{2}\) as the ETL, MAPbI\({}_{3}\) as the PAL, Cu\({}_{2}\)O as the HTL, and Au as the back contact. The energy band alignment of this structure is shown in Figure 1b. The work function (\(W/F\)) of ITO is \(-4.6\) eV, the lowest unoccupied molecular orbital (LUMO) in TiO\({}_{2}\) is at \(-3.9\) eV, and the LUMO in MAPbI\({}_{3}\) are at \(-3.9\) eV. Thus, the transfer of electrons to ITO was expected to proceed well. In addition, the highest occupied molecular orbital (HOMO) in MAPbI\({}_{3}\) is at \(-5.45\) eV, and the HOMO in Cu\({}_{2}\)O are at \(-5.37\) eV [55; 56; 57; 58]. The \(W/F\) of Au is \(-5.1\) eV [59]. Therefore, the migration of holes from the absorption layer to the Au electrode, which is the lower electrode, was also expected to proceed well.  
Table 1 shows the parameters of each layer used in the simulation here. Variables not specified in Table 1 are the thermal velocity of electrons/holes of 10\({}^{7}\) cm/s, the interface defect density of 1 \(\times\) 10\({}^{-13}\) cm\({}^{-3}\), the hole capture cross-section of the absorber/ETL of 10\({}^{-18}\) cm\({}^{2}\), the hole capture cross-section of the absorber/HTL of 10\({}^{-19}\) cm\({}^{2}\), the electron capture cross-section of the absorber/ETL of 10\({}^{-19}\) cm\({}^{2}\), and the electron capture cross-section of the absorber/HTL of 10\({}^{-18}\) cm\({}^{2}\). A series resistance of 1 \(\Omega\)-cm\({}^{2}\), shunt resistance of 4200 \(\Omega\)-cm\({}^{2}\), constant illumination of 1000 W/m\({}^{2}\), and operating temperature of 300 K at AM 1.5G were used [55].