This invention provides a process for growing Ge epitaixial layers on Si substrate by using ultra-high vacuum chemical vapor deposition (UHVCVD), and subsequently growing a GaAs layer on Ge film of the surface of said Ge epitaixial layers by using metal organic chemical vapor deposition (MOCVD). The process comprises steps of, firstly, pre-cleaning a silicon wafer in a standard cleaning procedure, dipping it with HF solution and prebaking to remove its native oxide layer. Then, growing a high Ge-composition epitaixial layer, such as Si0.1Ge0.9 in a thickness of 0.8 μm on said Si substrate by using ultra-high vacuum chemical vapor deposition under certain conditions. Thus, many dislocations are generated and located near the interface and in the low of part of Si0.1Ge0.9 due to the large mismatch between this layer and Si substrate. Furthermore, a subsequent 0.8 μm Si0.05Ge0.95 layer, and/or optionally a further 0.8 μm Si0.02Ge0.98 layer, are grown. They form strained interfaces of said layers can bend and terminate the propagated upward dislocation very effectively. Therefore, a film of pure Ge is grown on the surface of said epitaixial layers. Finally, a GaAs epitaixial layer is grown on said Ge film by using MOCVD.