## 3 Results and Discussion
Very small local shearing (with around only 1\({}^{\circ}\) level orientation difference) at the interfaces of the multiple-layered structures can be clearly seen. However, the SAED shows that the film is still perfectly single-crystalline. Strain can be relaxed mainly through this kind of local shearing instead of forming a great number of dislocations. Thus, we found that area without multiple-layered structures relaxed strain through typical strain relaxation mechanism shows many dislocations, while area with multiple-layered structures shows few dislocations and it may be under a non-typical strain relaxation mechanism. To understand the non-typical strain relaxation mechanism for Si\({}_{1-x}\)Ge\({}_{x}\) films grown by LT-MBE, we studied the intermediate products of a pure Ge film with multiple-layered structures. Figure 4 shows the HRTEM images of multiple-layered structures imaging along zone axis of [110]. We found that there were partial \"island growth,\" which left the hollow structures as shown in Figure 4I,II. Interestingly, the \"partial islands\" here are of approximately the same crystal orientation and finally merge into a single-crystalline structure during film growing (see Figure 4 III). Therefore, this growth process by short \"partial islands\" and their merging lead to the multiple-layered structure in the film. Although being well-limited, here the \"island growth\" still causes small local orientation variations [14; 15; 16], leading to the local shearing at the interfaces of the multiple-layered structures. And the local shearing effectively relaxes the strain, subsequently suppresses the dislocation density. Based on above discussions, we know that the non-typical strain relaxation mechanism is actually related to a partial \"island growth,\" which is strongly limited here (without any long pillar structures) and coexists with the typical strain relaxation mechanism. Figure 2: (**a**) XRD spectra of Si\({}_{0.5}\)Ge\({}_{0.5}\) and Ge films grown on Si (001); (**b**) The SAED and low-magnification TEM image of the Si\({}_{0.5}\)Ge\({}_{0.5}\) film grown on Si (001); (**c**,**d**) are AFM images of Si\({}_{0.5}\)Ge\({}_{0.5}\) and Ge films, respectively; (**e**,**f**) shows the typical etch pits distribution of the Si\({}_{1-x}\)Ge\({}_{x}\) thin films (x from 0.5 to 1), with TDD of 10\({}^{3-}\)10\({}^{4}\)/cm\({}^{2}\) level. The films were etched by Secco etchant. All films are 200 nm thick and grown at 200 \({}^{\circ}\)C.  
Figure 3: (**a**) Cross-sectional HRTEM image ([110]-zone) on an interface where strain is relaxed by dislocations; (**b**) zoom-in view of the red square marked in (**a**); (**c**) Cross-sectional HRTEM image ([110]-zone) an interface where strain is relaxed by the multiple-layered structures; (**d**) zoom-in view of the red square marked in (**c**). Yellow dotted lines highlight the interface of film and substrate. White dotted lines highlight the multiple-layered structures. Figure 5 shows the schematic 2D model of the Si\({}_{1-x}\)Ge\({}_{x}\) thin films grown on Si (001) relaxing strain through typical strain relaxation mechanism in an MBE grown heterostructure (circled in black on the left) together with the non-typical strain relaxation mechanism in an LT-MBE grown heterostructure (circled in black on the right). Red lines indicate the dislocations in the Si\({}_{1-x}\)Ge\({}_{x}\) film. Blue lines indicate the local shearing at interfaces of multiple-layered structures. And the formation of multiple-layered structures is similar to the formation of multiple-layered structures. Figure 4: [110]-zone cross-sectional HRTEM images of the pure Ge film intermediate products, which actually show the process of non-typical strain relaxation for Si\({}_{1-x}\)Ge\({}_{x}\) films grown by LT-MBE. structures refers to the formation of short islands along [-110] direction and then the short islands will afterwards crystallize into a single-crystalline structure. The light grey cubes near the Si\({}_{1-x}\)Ge\({}_{x}\) film surface indicate the short islands.