A heterostructure is provided which includes a substantially relaxed SiGe layer present atop an insulating region that is located on a substrate. The substantially relaxed SiGe layer has a thickness of from about 2000 nm or less, a measured lattice relaxation of from about 50 to about 80% and a defect density of less than about 10.sup.8 defects/cm.sup.2. A strained epitaxial Si layer is located atop the substantially relaxed SiGe layer and at least one alternating stack including a bottom relaxed SiGe layer and an top strained Si layer located on the strained epitaxial Si layer.