## 3 Results and Discussion
### Nanoscale Structural Properties  
The structural properties at the nanoscale were investigated by using TEM. Figures 7 and 8 give high- and low-resolution TEM images of the sample cross-section, respectively. Figure 7a shows a high-resolution TEM image, including the \(\varepsilon\)-Si and Ge\({}_{0.2}\)Si\({}_{0.8}\) layers. Three regions exist, each of which has a uniform contrast grade, and which corresponds to a dissimilar layer. The left lower region, which is brightest, is an epoxy resin layer of the sample that serves as the adhesive for the two wafers. The image shows no regular lattice structure in this region. The region adjacent to the epoxy is the \(\varepsilon\)-Si layer. The largest region in the image is the Ge\({}_{0.2}\)Si\({}_{0.8}\) layer. Inside the \(\varepsilon\)-Si layer, the lattice structure is complete and clear, and shows a regular mesh of the monocrystalline state. The growth surface is in the same atomic sheet. No visible defects exist in this layer. Moreover, the interface of the \(\varepsilon\)-Si/Ge\({}_{0.2}\)Si\({}_{0.8}\) layers appears clear, straight and almost atomically flat, where the lattices match well. The \(\varepsilon\)-Si layer thickness is relatively uniform at \(\sim\)8.67 nm. Figure 7 also shows that the cross-section is a (100) crystal plane. Figure 7: High-resolution transmission-electron microscopy (TEM) images of sample cross-section (**a**) at the \(\varepsilon\)-Si and Ge\({}_{0.2}\)Si\({}_{0.8}\) layers, (**b**) inside the Ge\({}_{0.2}\)Si\({}_{0.8}\) layer, (**c**) at the Ge\({}_{0.2}\)Si\({}_{0.8}\)/Ge\({}_{x}\)Si\({}_{1-x}\) interface and (**d**) inside the Ge\({}_{x}\)Si\({}_{1-x}\) layer. Figure 8a shows a low-resolution TEM image around the Ge\({}_{0.2}\)Si\({}_{0.8}\) layer, and Figure 7b shows a high-resolution enlarged image of spot **A** in Figure 8a, which is inside the Ge\({}_{0.2}\)Si\({}_{0.8}\) layer. In the low-resolution TEM image, no obvious defect exists inside the Ge\({}_{0.2}\)Si\({}_{0.8}\) layer. The interface between the Ge\({}_{\mathrm{x}}\)Si\({}_{1-\mathrm{x}}\) and Ge\({}_{0.2}\)Si\({}_{0.8}\) layers is clearly recognizable, which shows that the Ge\({}_{0.2}\)Si\({}_{0.8}\) layer thickness is uniform, at ~0.96 \(\mathrm{\SIUnitSymbolMicro m}\) (~1). According to the SEM, EDS and Raman results, as shown in Figures 1 and 3-7, the total thickness of the two GeSi buffer layers is 3.6 \(\mathrm{\SIUnitSymbolMicro m}\), and hence, that of the graded layer (Ge\({}_{\mathrm{x}}\)Si\({}_{1-\mathrm{x}}\)) is ~2.6 \(\mathrm{\SIUnitSymbolMicro m}\). In the high-resolution TEM images Figure 7a,b, the lattice phenomena in the Ge\({}_{0.2}\)Si\({}_{0.8}\) layer are analogous to those in the \(\varepsilon\)-Si layer. The two layers have the same lattice structure and dimensions and can only be distinguished according to differences in the contrast grades. The lattice maintained a good and similar crystal structure, which indicates that the stress in the \(\varepsilon\)-Si and Ge\({}_{0.2}\)Si\({}_{0.8}\) layers is not released by defects or dislocations. Figure 8b,c presents low-resolution TEM images around the Ge\({}_{\mathrm{x}}\)Si\({}_{1-\mathrm{x}}\) layer. Figure 7c,d presents high-resolution enlarged images at the Ge\({}_{\mathrm{x}}\)Si\({}_{1-\mathrm{x}}\)/Ge\({}_{0.2}\)Si\({}_{0.8}\) interface and at spot **B** in Figure 8b, respectively, where spot **B** is inside the Ge\({}_{\mathrm{x}}\)Si\({}_{1-\mathrm{x}}\) layer. In the low-resolution TEM image in Figure 8b,c, the interface between the Ge\({}_{\mathrm{x}}\)Si\({}_{1-\mathrm{x}}\) layer and C-Si substrate appears clear and straight. Numbers of dislocations exist in the Ge\({}_{\mathrm{x}}\)Si\({}_{1-\mathrm{x}}\) layer, especially close to the Ge\({}_{\mathrm{x}}\)Si\({}_{1-\mathrm{x}}\)/Si interface. Some appear as dislocation loops, such as the one in Figure 8d. Most dislocations connect and form dislocation networks inside the layer. Some vertical threading dislocation lines reach the Ge\({}_{\mathrm{x}}\)Si\({}_{1-\mathrm{x}}\)/C-Si interface.