G $e_{1-x}$ S $n_{x}$G $e_{1-y}$S $n_{y}$ is a very promising material for the high-speed device due to the fact that electron and hole mobilities for the strained G $e_{1-x}$ S $n_{x}$G $e_{1-y}$S $n_{y}$ are greatly enhanced. Because G $e_{1-x}$ S $n_{x}$G $e_{1-y}$S $n_{y}$ has a direct band gap for the proper combination of x and y, it can be applied to the optoelectronic device. Therefore, the study of the electrical property for G $e_{1-x}$ S $n_{x}$G $e_{1-y}$S $n_{y}$(001) with a direct energy gap is needed. G $e_{1-x}$ S $n_{x}$ layer can not be grown thickly due to the large difference of lattice constants. This fact prefers the structure of the device where electrons and holes move in the plane direction. The transverse mobilities of electron and hole for G $e_{0.8}$S $n_{0.2}$Ge(001) are 2~3 times larger than those for Ge/Ge/ sub0.8/S $n_{0.2}$(001). Therefore, G $e_{0.8}$S $n_{0.2}$Ge(001) is expected to be better than Ge/G $e_{0.8}$S $n_{0.2}$(001) for the development of the high-speed device.h-speed device.device.h-speed device. device.