## 3 Results and Discussion
The SDC has a fluorite structure with a lattice parameter of a\({}_{\text{SDC}}=\) b\({}_{\text{SDC}}=\) c\({}_{\text{SDC}}=\) 5.422 A [23], slightly larger than that of the GDC. In the 0-20 scan of the heterostructure, the presence of distinct SDC, STO, and SAO (001) diffraction peaks confirms the c-axis orientation of the entire multilayer structure. This result indicates that the sacrificial layer (SAO) and the underlying STO substrate played a critical role in guiding the epitaxial growth of the SDC layer. The high degree of orientation is essential for ensuring the desired functional properties of the heterostructure, as it minimizes defects that could impact performance. Figure 1: XRD patterns in 0-20 scan mode, respectively: (**a**) STO/SAO/STO and (**b**) STO onto PDMS. Figure 2: XRD patterns in 0-20 scan mode, respectively: (**a**) GDC/SAO/STO and (**b**) GDC onto PDMS. For the SDC layer, the observation of the (001) diffraction peak in the XRD pattern highlights its unique and superior crystallographic alignment compared to GDC. This suggests that the deposition process and epitaxial relationships in the multilayer system effectively promoted the formation of a well-ordered SDC structure. Such alignment is particularly important for applications that rely on anisotropic properties, such as ionic conductivity or electronic transport. After transferring the SDC layer to the flexible PDMS substrate, the XRD patterns demonstrate that the structural integrity and c-axis crystalline orientation of the SDC layer are largely preserved. This preservation is crucial for maintaining the layer's functionality in potential applications, such as flexible electronics, energy devices, or sensors. The successful retention of crystalline orientation suggests that the detachment process, which involves sacrificial layer etching and redeposition onto PDMS, was conducted with minimal mechanical or chemical damage to the SDC layer. The absence of secondary phases or additional orientations in the transferred SDC layer further validates the effectiveness of the transfer process. This result confirms that the multilayer system maintained its phase purity and avoided significant structural degradation, which could otherwise compromise its performance. The findings underscore the reliability of this approach for producing high-quality free-standing oxide layers with potential integration into flexible or unconventional substrates, enabling broader applications for epitaxial oxide materials. Figure 4 displays the RHEED patterns for the STO single-crystal substrate (Figure 4a), the SAO layer deposited onto the STO substrate (Figure 4b), and the SDC layer deposited onto the SAO/STO structure (Figure 4c) during PLD growth. The RHEED pattern of the SAO layer exhibits a streaky pattern, confirming the formation of a smooth, two-dimensional (2D) surface for the sacrificial layer (Figure 4b). This indicates that the deposition conditions were optimized to achieve a layer-by-layer growth mode, which is crucial for maintaining the structural integrity of the heterostructure and ensuring high-quality interfaces during subsequent processing steps. Figure 3: XRD patterns in 0-20 scan mode, respectively: (**a**) SDC/SAO/STO and (**b**) SDC onto PDMS. Additionally, in Figure 4b, the presence of superstructure streaks is evident, with these additional streaks spaced at one-quarter of the distance between the primary diffraction streaks corresponding to the STO lattice parameter. These superstructure lines indicate the formation of an in-plane lattice with a periodicity four times larger than that of the STO substrate. This observation is consistent with the lattice parameter of the SAO layer, which is approximately four times the STO lattice parameter. The appearance of these superstructure features demonstrates the epitaxial relationship between the SAO layer and the STO substrate, indicating a well-ordered lattice alignment and confirming the high crystalline quality of the SAO sacrificial layer.