## 3 Results and Discussion  
### Characterization of Triple-Cation Perovskite Thin Films  
#### 3.1.1 Structural Analysis of Triple-Cation Perovskite Thin Films  
The structural characteristics of the triple mixed-cation (Cs, FA, MA)-based perovskites were analyzed using X-ray diffraction (XRD). The XRD patterns in Figure 2 illustrate the changes in the crystal structure of the perovskite films as a function of the Cs content. The main diffraction peaks in the XRD patterns appeared at approximately 14.1\({}^{\circ}\) and 28.4\({}^{\circ}\), corresponding to the (110) and (220) planes of the perovskite structure, respectively. These peaks are similar to those of the double-cation (FAMAPbI\({}_{3}\)) perovskite, indicating that the perovskite crystal structure is well maintained in the triple mixed-cation system [20]. The incorporation of Cs, with a smaller ionic radius (1.81 A) than that of FA\({}^{+}\) (2.53 A), induces lattice contraction and forms a more compact crystal structure. This structural change can reduce the defect density and improve stability [21]. The main diffraction peaks are marked with asterisks in Figure 2 (at approximately 14.1\({}^{\circ}\) and 28.4\({}^{\circ}\)). Additionally, the main diffraction peaks of the \(\alpha\)-phase perovskite were maintained even after the incorporation of Cs. Notably, these \(\alpha\)-phase peaks remained visible at Cs concentrations of 0.05 and 0.10, suggesting that the triple mixed-cation structure may offer superior thermal and environmental stability than the double-cation structure. While the peak intensity of the Cs0.1 sample was slightly stronger than that of Cs0.05 (as shown in Figure 2c,d), the XRD results confirmed that the addition of Cs did not interfere with the formation of the perovskite crystal phase. Among the tested Cs compositions, Cs = 0.05 was found to be an optimal concentration that supported phase stability without introducing secondary phases. Similar trends have been reported in previous studies on triple-cation perovskite solar cells. For example, [PERSON] et al. reported that Cs incorporation contributes to lattice contraction and improved crystallinity while preserving the structural stability [22]. A follow-up study by the same group demonstrated that an optimal Cs content can enhance the photoelectric performance of both planar and mesoporous device structures [23]. These findings are consistent with our structural analysis, which suggests that moderate Cs incorporation leads to uniform and stable perovskite films. Considering the Goldschmidt tolerance factor and octahedral factor values, the Cs-incorporated perovskite structure remained within a stable range, indicating that the Cs addition did not adversely affect the structural stability of the double-cation perovskite. The XRD patterns revealed that no secondary phases were induced by Cs incorporation, confirming the successful formation of a homogeneous and stable triple-cation perovskite. The Goldschmidt tolerance factor (\(t\)) and octahedral factor (\(\mu\)) were calculated to evaluate the crystal structures of the Cs, FA, and MA triple-cation (CsFAMAPbI\({}_{3}\)) perovskites [20]. Table 1 shows the variations in the tolerance and octahedral factors for the bare (FAMAPbI\({}_{3}\)) and Cs-doped conditions (Cs0.03, 0.05, and 0.10). The Goldschmidt tolerance factor is defined as  
\[t=\frac{r_{A}+r_{X}}{\sqrt{2}(r_{B}+r_{X})}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Cs Content** & **Tolerance Factor (\(t\))** & **Octahedral Factor (\(\mu\))** \\ \hline Bare (FAMAPbI\({}_{3}\)) & 0.98 & 0.54 \\ \hline
0.03 & 0.97 & 0.54 \\ \hline
0.05 & 0.97 & 0.54 \\ \hline
0.10 & 0.96 & 0.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Goldschmidt tolerance and octahedral factors after Cs addition. Figure 2: XRD patterns of mixed-cation perovskite films with varying Cs contents: (**a**) Cs\({}_{0}\).00 (bare), (**b**) Cs0.03, (**c**) Cs0.05, and (**d**) Cs0.10.