## 3 Results and Discussion  
### Microscale Structural Properties  
Figure 1b shows an SEM image of the multilayer vicinity of the cross-sectional sample. Because of differences in the electrical resistance of each layer, distinctive monocrystalline silicon, Ge\({}_{\mathrm{x}}\)Si\({}_{\mathrm{1-x}}\), Ge\({}_{\mathrm{0,2}}\)Si\({}_{\mathrm{0,8}}\) and epoxy resin layers were observed. A narrow black strip of \(\sim\)1 \(\upmu\)m thickness is the adhesive layer of epoxy resin that adheres the two multilayer wafers. The region with uniform and relatively deeper greyscale, at the left of the image and far from the adhesive layer, is the C-Si substrate. From the C-Si substrate to the wafer edge (\(\sim\)3.6 \(\upmu\)m thickness), the grayscale becomes brighter gradually, which is the graded and relaxed buffer layers. The C-Si/Ge\({}_{\mathrm{x}}\)Si\({}_{\mathrm{1-x}}\) interface is clear and straight, but that of the Ge\({}_{\mathrm{x}}\)Si\({}_{\mathrm{1-x}}\)/Ge\({}_{\mathrm{0,2}}\)Si\({}_{\mathrm{0,8}}\) interface is barely distinguishable visible in this SEM image. The strained-silicon layer (\(\sim\)10 nm thick) is not recognized in the SEM image, because of the resolution limitation of the SEM system. The SEM image also shows that there is no visible fluctuation on the surface of the sample cross-section. The cross-sectional surface roughness was measured by using an atomic-force microscope (AFM, Dimension Icon, Bruker, Billerica, Massachusetts, USA) and a white-light interferometer (WLL, NewView 8300, Zygo, Middlefield, Connecticut, USA). Figure 2a gives the height data of a random 500 nm \(\times\) 500 nm area on the cross-sectional surface detected by AFM. The root-mean-square deviation of the height data (Rq) is 0.43 nm, and the arithmetical mean deviation of the height data (Rq) is 0.33 nm. Figure 1: (**a**) Schematic structure of prepared \(\varepsilon\)-Si/GeSi/C-Si material, (**b**) scanning-electron microscopy (SEM) image of multilayer vicinity of sample cross-section. CVE, chemical vapor epitaxy. Figure 2b gives the height data of a random 21 \(\upmu\)m \(\times\) 21 \(\upmu\)m area on the cross-sectional surface detected by using a white-light interferometer with a spatial resolution of 0.34 \(\upmu\)m in the \(X/Y\) direction and 0.01 nm in the \(Z\) direction (root-mean-square repeatability). Rq and Ra are essential surface-roughness parameters. The experimental results showed that the surface roughness of the sample cross-section was less than 0.5 nm, regardless of the nano- or microscale area. The elemental distribution along the depth direction of the sample cross-section is shown in Figure 3 as determined by EDS (Oxford Instruments, Oxford, UK) with a 42-nm step length. When the EDS sampling point on the cross-section surface approaches the wafer edge, the elemental silicon content exhibits an approximately linear decrease and that of elemental germanium shows a linear increase. Such linear variations of the elemental components that are sustained inside a region of -2.6 \(\upmu\)m in thickness, corresponding to the graded buffer layer (via the Ge\({}_{\times}\)Si\({}_{1-\times}\) layer). The content of elemental silicon increased slightly and gradually until the sampling point reached the wafer edge. The opposite behavior resulted in the content of elemental germanium. The thickness of this region was \(\sim\)1 \(\upmu\)m, which corresponds to the relaxed buffer layer (viz. the Ge\({}_{0.2}\)Si\({}_{0.8}\) layer). In this layer, the actual distributions of elemental Si and Ge did not agree with, but were not distinct  
Figure 3: Elemental distribution along the depth direction achieved by using energy-dispersive spectroscopy (EDS). Figure 2: The surface roughness of cross-sectional surface measured by (**a**) atomic-force microscope (AFM) and (**b**) white-light interferometer. from, the design shown in Figure 1. The EDS result showed that it was difficult to recognize the interface between the two buffer layers, and the exact thickness of the two buffer layers.