## 3 Results and Discussion  
We have conducted a series of experiments to find out the \"proper\" growth temperature for different Ge contents. Si1\({}_{-x}\)Ge\({}_{x}\) films (20 nm thick) with x equals to 0.67 and 0.74 at growth temperatures of 100 \({}^{\circ}\)C, 200 \({}^{\circ}\)C, 300 \({}^{\circ}\)C, and 500 \({}^{\circ}\)C, respectively, were studied by XRD (see Figure 1). We have found that the full width at half maximum (FWHM) decreases as temperature decreases and AFM study (not shown here) also shows that the surface becomes smoother as temperature decreases down to 200 \({}^{\circ}\)C. Furthermore, for both Si0\({}_{3.33}\)Ge0\({}_{0.67}\), and Si0\({}_{2.26}\)Ge0\({}_{0.74}\) films grown at 200 \({}^{\circ}\)C, the fringes in the XRD spectra evidently indicate the well-crystallized interface between Si1\({}_{-x}\)Ge\({}_{x}\) film and Si buffer layer. The film quality of the samples grown at 100 \({}^{\circ}\)C is comparable to the ones grown at 200 \({}^{\circ}\)C. As the growth temperature goes lower than a certain point, crystallization cannot be guaranteed beyond a critical thickness. Based on our study and the discussions above, we finally selected 200 \({}^{\circ}\)C as the \"proper\" low temperature for all the following film growth. Figure 2a shows typical XRD spectra scanned from Si0\({}_{0.5}\)Ge0\({}_{0.5}\) and Ge films grown on Si (001). Peaks of Si0\({}_{0.5}\)Ge0\({}_{0.5}\) (004), Ge (004), and substrate Si (004) can be recognized. Figure 2b shows the low-magnification TEM image of Si0\({}_{0.5}\)Ge0\({}_{0.5}\) film grown on Si (001). The selected area electron diffraction pattern (SAED) of Si0\({}_{0.5}\)Ge0\({}_{0.5}\) film grown on Si (001) with zone axis of [110] is also shown and the SAED indicated the good coherency of the epitaxial growth. Figure 2c,d are AFM images of 4 \(\upmu\)m \(\times\) 4 \(\upmu\)m area of Si0\({}_{0.5}\)Ge0\({}_{0.5}\) and Ge films. It can be seen that no island growth occurred, and the film surface roughness remained in a few nanometers. The chemical etchant for TDD estimation was Secco etchant (1 part 0.15 mol/L K\({}_{2}\)Cr2O\({}_{3}\): 2-part 48% HF by volume) and etching time was 30 s. By counting the number of etch pits, TDD can be obtained as \(3.33\times 10^{3}\)/cm\({}^{2}\) and \(1.67\times 10^{4}\)/cm\({}^{2}\). The optical microscope images of typical Si1\({}_{-x}\)Ge\({}_{x}\) films after etching are shown in Figure 2e,f, respectively. We chose three areas and took optical images. Here, the typical error bar is about \(\pm\)10%. The TDD shows an average value of  
As the dislocations nucleate at the free surface and glide to the interface, the atomic structure of dislocation at the heterointerface determines its electronic properties. In diamond structure, edge dislocations have higher core energy, thus strain relaxation prefers to occur by introducing 60\({}^{\circ}\)-mixed dislocations which lie on [111] gliding planes instead of edge dislocations. The misfit segments run in the \(<\)110\(>\) direction and the threading arms run up to the surface [24; 34; 35]. As Figure 3a shows, some 60\({}^{\circ}\) dislocations gliding towards the interface can be seen. For Si\({}_{1-x}\)Ge\({}_{x}\) films grown on Si (001) by MBE under typical strain relaxation mechanism, as Ge content increases, lattice mismatch increases and more misfit dislocations at the interface and threading dislocations in the epilayer form. Figure 3a shows a HRTEM image of interface with dislocations and Figure 3b highlights the dislocation core. However, in this study, with the use of LT-MBE to grow Si\({}_{1-x}\)Ge\({}_{x}\) films on Si (001), instead of seeing a great number of dislocations in the film due to large mismatch strain, an area containing multiple-layered structures and few dislocations were observed, as shown in Figure 3c. Figure 3d is the interface of Ge film and Si buffer layer containing multiple-layered structures and few dislocations.