## 3 Results and Discussion
Moreover, the observation of these superstructure lines provides valuable insight into the lattice matching and strain accommodation mechanisms at the SAO/STO interface. This alignment is critical for ensuring that subsequent layers, such as the SDC layer, allow the high crystallinity and smooth morphology necessary for advanced functional devices. These results are indicative of the optimized growth parameters to achieve precise surface quality control and ensure the application of this technique to the realization of complex heterostructures. In contrast, the initial growth of the SDC layer displayed characteristics of three-dimensional (3D) island growth, as expected for the first 20-30 unit cells due to the lattice mismatch or differences in surface energy. However, as the deposition progressed, the RHEED pattern transitioned to streaky lines, signifying the evolution from a 3D to a 2D growth mode (Figure 4c). The ability of the SDC layer to achieve a 2D growth mode after the initial 3D growth phase is critical for ensuring a high-quality crystalline film suitable for subsequent applications. The RHEED observations indicate the precise control over growth parameters needed to achieve high-quality surfaces and interfaces within the heterostructure, which are essential for its functional performance. Figure 5 presents the FE-SEM images of the SDC membrane transferred onto the PDMS substrate. Although the SDC film was successfully and entirely transferred onto the flexible PDMS, cracks are apparent in the FE-SEM images. These cracks are likely caused by mechanical stresses during the transfer process or strain relaxation as the film detaches from the rigid substrate. Such defects could influence mechanical robustness and limit the potential applications of the membrane in devices that demand structural continuity and reliability. At higher magnification, as shown in the inset of Figure 5b, single-crystal SDC  
Figure 4: The Reflection High-Energy Electron Diffraction (RHEED) pattern evolution during the PLD process: STO (100) single crystal (**a**); SAO/STO (**b**); SDC/SAO/STO (**c**). flakes with a distinctive square shape are observed. The square morphology reflects the cubic symmetry of the SDC crystal structure, highlighting its well-preserved crystallographic features. This observation suggests that, despite the presence of cracks, the crystalline quality of the SDC layer remains largely unaffected by the transfer process. The retention of these structural characteristics shows the effectiveness of the growth and transfer protocols in maintaining the film's intrinsic properties, which is essential for its performance in applications such as ionic conductors, solid oxide fuel cells, or thin-film-based electronic devices. To further enhance the quality of the transferred membranes, improvements in the transfer process could focus on minimizing cracking. Such optimization would enable the production of high-quality, flexible membranes tailored for advanced technological applications. The sacrificial layer method gives the possibility to evaluate the transport properties of the materials in a free-standing configuration without any interfacial contribution due to the presence of the substrate and or the bottom layer in a heterostructure configuration. Figure 6 illustrates step by step a possible procedure to make electrochemical devices with the sacrificial layer method based on a free-standing membrane:  
1. Step 1: PLD deposition of the water-soluble sacrificial Sr\({}_{3}\)Al\({}_{2}\)O\({}_{6}\) (SAO) onto STO single crystals. 2. Step 2: PLD deposition of the electrolyte layer, which is a pure O\({}_{2}\)- conductor with the scope to separate the current collector from the bottom of the cell, preventing a shortcut in the electrochemical cell [10; 24; 25]. 3. Step 3: PLD deposition of the cathode layer (SDC or GDC). 4. Step 4: PDMS is glued onto the surface of the film, and the sacrificial layer SAO is etched in distilled water solution to detach the STO substrate. 5.