## 3 Results and Discussion  
Initially, to optimize the deposition parameters of SAO, only the SAO layer was deposited. However, it was necessary to prevent its exposure to ambient humidity, as the SAO layer degraded rapidly once removed from the deposition chamber. To mitigate this issue, a crystalline STO cap layer was deposited on top of the SAO layer to protect it from degradation caused by humidity. SAO has a cubic structure with a lattice constant of \(\mathrm{a_{SAO}=b_{SAO}=c_{SAO}=15.844}\) A [1]. This lattice parameter is almost equal to four times the STO lattice parameter (\(\mathrm{c_{STO}=3.905}\) A): \(\mathrm{c_{SAO}=4\times c_{STO}}\). Figure 1a presents the XRD patterns in \(\theta\)-20 scan mode for the STO/SAO/STO (001) heterostructure. The SAO peaks observed in the \(\theta\)-20 scan confirm the \(\mathrm{c}\)-axis orientation of the sacrificial SAO layer in the STO/SAO bilayer. The diffraction peak of the STO layer deposited on the SAO sacrificial layer is superimposed on the STO (001) substrate single-crystal peak, indicating that the STO layer replicates the orientation of the underlying substrate. The insets in Figure 1a provide a closer view of the XRD patterns, highlighting the SAO (004) and SAO (008) peaks, which further confirm the high crystallographic quality of the SAO layer. The c-lattice parameter obtained by these diffraction peaks is c = 15.82 A [12]. This value is in agreement with the values found in the literature. These results suggest that the epitaxial relationship between the SAO sacrificial layer and the STO substrate is well maintained. A PDMS Gelpack adhesive polymer was applied onto the STO film surface of the heterostructure STO/SAO/STO. The heterostructure was then immersed in water to dissolve the SAO to obtain an STO free-standing membrane. Figure 1b displays the XRD patterns in \(\theta\)-20 scan mode for the STO membrane transferred onto a PDMS wafer. The presence of the (001) and (002) diffraction peaks corresponding to the STO layer confirms the successful transfer process. Additionally, the calculated c-lattice parameter for STO on PDMS (c = 3.92 A) is slightly larger compared to the bulk value (c = 3.905 A), likely due to compressive strain induced by the non-flat nature of the PDMS substrate. These results highlight the structural integrity of the STO layer and demonstrate the successful transfer of high-quality free-standing membranes onto a different support. Furthermore, they confirm the feasibility of using SAO as a sacrificial layer for the subsequent transfer of SDC and GDC thin films. Following this initial step of optimizing the deposition parameters for SAO, we proceeded with the fabrication of the heterostructure GDC/SAO on an STO (100) substrate. The GDC has a fluorite crystal structure with a lattice parameter of \(\mathrm{a_{GDC}=b_{GDC}=c_{GDC}=5.412}\) A [23]. Figure 2 shows the XRD patterns obtained in \(\theta\)-20 scan mode for the GDC/SAO/STO (100) heterostructure. The \(\theta\)-20 scan reveals the SAO (00l) diffraction peaks, confirming the c-axis orientation of the SAO sacrificial layer within the heterostructure. Additionally, the diffraction pattern in Figure 2a indicates two orientations for the GDC layers (111) and (002), highlighting the coexistence of different crystalline domains during growth. The presence of (111) reflection in the GDC/SAO/STO (100) heterostructure can be attributed to the strain induced by the underlying SAO layer and/or the STO substrate. In contrast, the XRD \(\theta\)-20 scan for the GDC layer transferred onto the PDMS substrate shows only the (001) orientation (Figure 2b), indicating a single crystallographic orientation after transfer. This could be attributed to the relaxation of residual stresses or the influence of the flexible PDMS. Figure 3a,b present the X-ray diffraction patterns in 0-20 scan mode for the SDC/SAO/ STO (001) heterostructure and the SDC layer transferred onto PDMS, respectively.