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Generation of residual stress in thin films: Residual stress in thin films is a common phenomenon that occurs during their production and fabrication processes. Regardless of coating techniques such as chemical vapor deposition, physical vapor deposition, or magnetron sputtering, residual stress in the film is inevitable. Film stress is a macroscopic phenomenon, yet it can reflect the internal state of the deposited film. The presence of residual stress in the film affects its quality and performance. Film stress is usually divided into tensile stress and compressive stress. For example, residual tensile stress in the thin film can exacerbate stress concentration within the material, promoting the initiation of cracks or accelerating the growth of microcracks ； Residual compressive stress can relieve stress concentrations within the material, thereby improving its fatigue resistance; however, excessive compressive stress can cause the film to bubble or delaminate. Regardless of the coating method used, when the film material is deposited on a substrate via vapor deposition in a vacuum chamber, this phase change from gas to solid causes a significant change in the volume of the film material. This change, combined with the compression or stretching between the deposited atoms (or molecules), leads to the formation of microholes and defects during the film-forming process, thereby generating internal stresses. After the coating process is completed, as the temperature inside the coating machine drops from a high level to room temperature, differences in the coefficients of thermal expansion between the film and the substrate lead to mismatched amounts of contraction or expansion, thereby generating thermal stress. Thermal stress is caused by the difference in thermal expansion coefficients between the thin film and the substrate material, which is why it is also referred to as thermal mismatch stress. The coefficient of thermal expansion is an inherent property of materials, and it can vary significantly among different types of materials. This difference is the main cause of residual stress generated during the epitaxial growth of the film on the substrate. Internal stress, also known as intrinsic stress, has a relatively complex origin. Currently, there are several theoretical models for the causes of internal stress. (1) Thermal shrinkage effect model: The premise of the stress generation model due to thermal shrinkage is that the top layer of the film reaches a quite high temperature during evaporation deposition. During the film formation process, the evaporated gas-phase atoms deposited onto the substrate possess high kinetic energy; thermal radiation generated from the evaporation source, etc., causes the temperature of the film to rise. When the deposition process is complete, as the film cools to the temperature of the surrounding environment, the atoms gradually become unable to move. The critical criterion for whether atoms within a film can move is the recrystallization temperature; thermal contraction below this temperature is what causes stress. (2) Phase transfer effect model: During the formation of thin films, a transfer from the gas phase to the solid phase occurs. Depending on the evaporated film material, it can be further divided into transitions from the gas phase to the liquid phase and then to the solid phase, as well as transitions from the gas phase to the liquid phase, then to another solid phase. Volume changes generally occur during phase transitions, thereby inducing stress. (3) Model for the elimination of lattice defects Thin films often contain many lattice defects; defects such as vacancies and interstices are eliminated through annealing, as atoms diffuse across the surface, which leads to volume contraction and the formation of internal stresses with tensile properties. (4) Surface tension and intergranular boundary relaxation model: During the initial nucleation and growth stages of film formation, since the atoms within the islands as well as the islands themselves are mobile, no internal stress can be generated ； As the island grows larger, the bond between it and the substrate strengthens. At this point, not only is the movement of atoms or the island itself restricted, but the crystallization of the island is also inhibited due to surface tension, thereby generating compressive stress ； As the islands grow larger further, the distance between them decreases, which increases the gravitational force and thus generates tensile stress ； Tensile stress reaches its maximum when islands approach each other to form grain boundaries. Thereafter, if the grain boundary condition remains unchanged, the stress stays constant. (5) Interface mismatch model: When a thin film material with a significantly different lattice structure from that of the substrate forms a film on this substrate, and if the interaction between the two is strong, the lattice structure of the thin film will approach that of the substrate. As a result, large distortions occur within the thin film, leading to internal stresses. If the degree of mismatch is small, uniform elastic deformation occurs ； Conversely, if the degree of mismatch is high, interfacial dislocations will be generated, thereby relieving most of the strain in the thin film. This interface mismatch model is generally used to explain the generation of stress during the epitaxial growth of single-crystal thin films. (6) Impurity effect model: During the formation of thin films, the presence of gases such as oxygen, water vapor, and nitrogen in the ambient atmosphere can cause changes in the structure of the thin film. For example, the adsorption of impurity gas atoms or their retention in the film results in interstitial atoms, causing lattice distortion; these atoms may also diffuse and migrate within the film, and chemical reactions such as grain boundary oxidation may occur. The more residual gas is incorporated into the film as an impurity, the easier it is for large compressive stress to be generated. Additionally, due to intergranular diffusion, impurity diffusion can occur even at low temperatures, thereby generating compressive stress. (7) Atomic and ionic pinning effect model: During the thin film sputtering deposition process, the most notable feature is the presence of working gas atoms, and the energy of the sputtered atoms is relatively high. Under low working pressure or negative bias conditions, films in a compressive stress state are typically obtained; this compressive stress is generally the inherent stress in sputtered films.