Strained silicon (ε-Si) is a promising material that could extend Moore's law by enhancing electron mobility. A ε-Si material is usually composed of multiscale, multilayer heterostructures, where the strained-silicon film or strap is tens-of-nanometers thick, and its buffer layers are of the micrometer scale. The structural properties determine the electrical performance and reliability of ε-Si-based devices. Inhomogeneous residual stress is induced during the preparation, which induces ε-Si structure failure. In this work, biaxial strained-silicon films that contain graded and relaxed germanium-silicon buffer layers were prepared on monocrystalline silicon wafers through reduced-pressure chemical-vapor epitaxy. The layer components and thicknesses were measured using energy-dispersive spectroscopy and scanning-electron microscopy. Crystal and lattice characters were observed by using high-resolution transmission-electron microscopy and micro-Raman spectroscopy. The residual stress distribution along cross-sections of the ε-Si multilayer structures was examined by using micro-Raman mapping. The experimental results showed that, with a gradual increase in germanium concentration, the increasing residual stress was suppressed owing to dislocation networks and dislocation loops inside the buffer layers, which favored the practical application. may yield a material/structure that meets the design requirements of geometrical dimensions and structural-mechanical properties [7,8]. Furthermore, the design, manufacture, performance evaluation and control technologies for microelectronics with non-uniform and local-singular stress distribution is regarded as the future of the microelectronics industry [9].The (equal biaxial or uniaxial) strain state and its magnitude determine the optical/electrical properties of ε-Si-based devices [10]. The strain state and magnitude of the ε-Si depend heavily on the buffer-layer properties (such as the element composition, thickness, lattice quality, defects and residual stress) and interfacial properties (such as mismatch and shear stress) [11]. Size miniaturization of a ε-Si-based device leads to increased defect densities and residual stress, which results in a degraded optoelectronic performance and structure reliability of the entire integrated device [12].Experimental studies of multilayer heterogeneous structures, such as strained-silicon, face two major challenges, namely, "multiscale" and "multiproperty coupling". A strained-silicon layer is usually several to tens-of-nanometers thick, whereas the buffer-layer thickness tends to be of the micrometer scale, and the substrate is typically several hundreds of microns thick. Unique key physical and mechanical behaviors that interact exist at each spatial scale. Cross-scale interactions between the multiscale physical-mechanical properties increase the complexity of experimental studies of strain silicon.A number of methods at different spatial scales have been applied to experimental studies on multilayer heterogeneous structures [1...