## 1 Introduction  
Strained silicon (\(\varepsilon\)-Si) is regarded as a promising material that could extend [PERSON]'s law [1]. Because introduced strain leads to an increased carrier mobility and reduced resistance [2], the performance of \(\varepsilon\)-Si-based devices is improved significantly [3]. In recent years, with continuous developments in \(\varepsilon\)-Si technology, semiconductor chips have become smaller, faster, and more energy efficient [4]. Strained-silicon technology has been applied widely in core chips inside mobile phones, personal computers, laptops, tablets and even televisions [5]. The \(\varepsilon\)-Si structure complexity determines the difficulty of the manufacturing process. In general, \(\varepsilon\)-Si is achieved by manufacturing a set of multiscale, multilayer heterogeneous two- or three-dimensional structures [6]. The manufacture of such a complex structure requires a strict and well-designed control of process parameters to ensure that each processing procedure step 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 \(\varepsilon\)-Si-based devices [10]. The strain state and magnitude of the \(\varepsilon\)-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 \(\varepsilon\)-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 [13; 14; 15; 16]. The profiler has been used to measure the average residual stress from the mesoscale [17]. By using (scanning- and transmission-) electron microscopy, the structural morphology and dislocation distribution in the microscale have been determined [18]. At the same scale, nano-indentation has been used to measure the modulus [19], whereas Raman microscopy has been applied to characterize the lattice quality and residual stress [20; 21; 22]. High-resolution transmission-electron microscopy (TEM) has been used to analyze the lattice structure and local strain of materials at the nanoscale [23]. However, most widely used experimental methods can measure or characterize only one or several material parameters at their respectively applicable scales. These techniques do not provide sufficient understanding of the multiscale structure properties, such as strained silicon, and it is difficult to discover the interaction between the different structural and mechanical properties at different spatial scales. Therefore, there is a need for collaborative analysis using methods at different spatial scales to investigate the interaction mechanisms of multiproperty coupling.