## 1 Introduction  
In recent decades, there has been growing interest in integrating functional oxides with semiconductor devices. This interest is driven by the increasing demand for combining functional layers produced through different techniques. It is crucial to fabricate and interconnect layers with different functionalities and integrate them into devices. However, achieving the integration of optimal materials presents significant challenges, as high crystal quality and minimal interfacial defects are often necessary to enhance device performance. Epitaxial oxide layers can only be fabricated when the substrate's crystal symmetry provides a compatible lattice parameter. The lattice mismatch between functional layers limits the integration of different materials and their applications. Moreover, the challenges of producing integrated devices become even more significant when attempting to combine dissimilar layers. Oxides and semiconductors are just two examples of materials whose integration can be particularly difficult. A promising solution to these challenges is the production of free-standing oxide membranes using the sacrificial layer method. These membranes can be manipulated, bent, stretched, and folded to tailor their properties. More importantly, free-standing membranescan be transferred onto otherwise incompatible substrates. This enables the design of a new generation of devices assembled by stacking free-standing oxide membranes [1; 2; 3; 4; 5]. The ability to engineer and fabricate high-quality functional oxide membranes is essential for advancing this new generation of devices that integrate functional layers into multilayer stacks. The stacking capability and strain tunability of these membranes can significantly enhance physical properties in engineered silicon-based devices. A particularly effective method for producing free-standing membranes involves using water-soluble tristrontium dialumuminum hexaoxide (Sr\({}_{3}\)Al\({}_{2}\)O\({}_{6}\), SAO) as a sacrificial layer. The lattice of SAO (cubic, a = 15.844 A [1]) matches the equivalent of four unit cells of common functional perovskite oxides, such as SrTiO\({}_{3}\), La\({}_{3}\)Sr\({}_{1,\text{-}}\)MnO\({}_{3}\), BiFeO\({}_{3}\), and LaNiO\({}_{3}\), facilitating epitaxial growth [2; 3; 4; 5; 6; 7]. It is worth noting that the silicon micromachining technique can also be employed to fabricate free-standing membranes. After the deposition of the functional oxide layer, silicon can be etched to produce the free-standing membrane [8]. However, silicon micromachining often results in poor crystallographic quality of the oxide thin film deposited on silicon substrates. Furthermore, PLD growth conditions, such as oxygen partial pressure and deposition temperature, can significantly affect the properties of the silicon substrate. Recently, the epitaxial lift-off technique has emerged as another approach to obtaining free-standing membranes. This method allows epitaxial layers to be transferred and rotated at different twist angles. When these layers are periodically stacked with varying orientations, they can form a new class of super-lattices with novel and tunable properties arising from the interfaces between the twisted layers [5; 9]. Recently, the interest in sacrificial layers, coupled with the growing demand for miniaturized devices in energy storage and conversion, has made the advancement of thin-film technologies strategically important for the development of micro-electrochemical devices such as micro-Solid Oxide Fuel Cells (m-SOFCs) and micro-Solid Oxide Electrochemical Cells (m-SOECs) [8; 9; 10; 11; 12; 13]. As a result, strontium aluminate Sr\({}_{3}\)Al\({}_{2}\)O\({}_{6}\) (SAO) has gained significant attention as an effective sacrificial layer in the fabrication of free-standing thin-film membranes.