# Effects of Adding Alkali Metals and Organic Cations to Cu-Based Perovskite Solar Cells
## 3 Results and Discussion  
First-principles calculated band structures and partial density of states are shown in Figure 1; parameters are listed in Table 1. Figure 1a-d shows the effects of halogen substitution. For MAPbJ\({}_{3}\), the energy gap increased when I was replaced with Br or Cl. An increase in the energy gap would increase the open-circuit voltage. Both the effective mass ratio of electrons, in the case of total Br substitution, and that of holes, in the case of total Cl substitution, increased relative to those values for MAPbJ\({}_{3}\). Because of the inverse relationship between effective mass and carrier mobility, it was expected that carrier mobilities would decrease when Br or Cl was added. However, for the three halogens in MAPbClBrI in Figure 1d, the effective mass ratios of the carriers were not significantly different from those of MAPbI3, and the energy gap increased. Table 1 shows the total energy per unit cell of the structure model; a small value indicates a more stable crystal structure. Therefore, because the total energy decreased by replacing I with Br or Cl, the crystal structure was expected to be more stable. Figure 2a-c shows the calculated results when the organic and metal cations were replaced with EA and Cu. The horizontal axis of the figure represents the wavenumber vector, and each symbol represents a symmetry point in reciprocal lattice space, as follows: \(\Gamma\) (0, 0, 0), X (0, 1/2, 0), M (1/2, 1/2, 0), and R (1/2, 1/2, 1/2). The addition of EA increased the crystal stability, in good agreement with previous studies [30]. When Pb was replaced by Cu, the hole mobility was expected to increase. However, the crystal stability would decrease. For EACul3 in Figure 1c, the total energy was lower than that of MACul3, indicating structure stabilization by EA substitution in the presence of Cu. Figure 1: Calculated band structures and DOS of (**a**) MAPbI3, (**b**) MAPbBr3, (**c**) MAPbCl3, and (**d**) MAPbClBrI. Figure 3a-d shows the calculated results when the organic cation was replaced by an alkali metal. Although there were no significant differences in the resulting parameters, there was a difference in the energy level of the alkali-metal band that was formed slightly above the conduction band minimum. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Total Energy (keV)** & **Energy Gap (eV)** & \(m_{\text{e}}\)*/\(m_{\text{o}}\) & \(m_{\text{h}}\)*/\(m_{\text{o}}\) \\ \hline MAPbI\({}_{3}\) & \(-3.50\) & \(1.51\) & \(0.071\) & \(0.100\) \\ MAPbBr\({}_{3}\) & \(-3.66\) & \(2.26\) & \(0.224\) & \(0.100\) \\ MAPbCl\({}_{3}\) & \(-3.78\) & \(2.75\) & \(0.144\) & \(0.462\) \\ MAPbClBrI & \(-3.64\) & \(2.03\) & \(0.092\) & \(0.102\) \\ MACuI\({}_{3}\) & \(-2.52\) & \(1.48\) & \(0.136\) & \(0.079\) \\ EAPbI\({}_{3}\) & \(-3.68\) & \(1.43\) & \(0.076\) & \(0.104\) \\ EACuI\({}_{3}\) & \(-2.71\) & \(1.42\) & \(0.097\) & \(0.080\) \\ NaPbI\({}_{3}\) & \(-2.99\) & \(1.06\) & \(0.077\) & \(0.062\) \\ KPbI\({}_{3}\) & \(-3.00\) & \(1.04\) & \(0.068\) & \(0.062\) \\ RPbI\({}_{3}\) & \(-3.00\) & \(1.03\) & \(0.067\) & \(0.062\) \\ CsPbI\({}_{3}\) & \(-3.00\) & \(1.00\) & \(0.067\) & \(0.061\) \\ \hline \end{tabular}
\end{table} 
Table 1: Calculated parameters of various perovskite compounds. Figure 2: Calculated band structures and DOS of (**a**) MACuI\({}_{3}\), (**b**) EAPbI\({}_{3}\), and (**c**) EACuI\({}_{3}\). The calculated band structures and partial density of states of the partial-substitution structure models are shown in Figure 4. These models contained more atoms than the total-substitution structure models, and thus required more time for the band calculations. In contrast to Figure 4a, where one of the eight MA molecules was replaced with EA, the addition of Cu resulted in the formation of a shallow band of Cu d-orbitals slightly above the band of I p-orbitals. This decreased the energy gap and hole mobility.