A method and a layered heterostructure for forming high mobility Ge channel field effect transistors is described incorporating a plurality of semiconductor layers on a semiconductor substrate, and a channel structure of a compressively strained epitaxial Ge layer having a higher barrier or a deeper confining quantum well and having extremely high hole mobility for complementary MODFETs and MOSFETs. The invention overcomes the problem of a limited hole mobility due to alloy scattering for a p-channel device with only a single compressively strained SiGe channel layer. This invention further provides improvements in mobility and transconductance over deep submicron state-of-the art Si pMOSFETs in addition to having a broad temperature operation regime from above room temperature (425 K) down to cryogenic low temperatures (0.4 K) where at low temperatures even high device performances are achievable.