We have investigated the growth and crystalline properties of tensile-strained Ge and Ge1-xSnx heteroepitaxial layers for high-mobility channels. The low temperature growth and the large misfit strain between Ge1-xSnx and Si leads to the high density of defects such as vacancy in Ge1-xSnx layers. They effectively enhance the propagation of misfit dislocations and the strain relaxation with suppressing the precipitation of Sn atoms from Ge1-xSnx layers. As a result, we succeeded in growing strain-relaxed Ge1-xSnx layers with a Sn content over 9% by controlling the dislocation structures. We also characterized the Hall mobility of Ge1-xSnx layers and found that the Sn incorporation into Ge effectively reduced the concentration of holes related to vacancy defects, and improved on the hole mobility.