Strained silicon technology employing strain-relaxed SiGe virtual substrates has become pivotal for advancing Group IV semiconductor electronics, photonic devices, silicon-based quantum computing architectures, and neuromorphic devices. While existing approaches using Si/SiGe superlattice buffers and compositionally graded SiGe layers enable the fabrication of high-quality SiGe virtual substrates, defects including threading dislocations and crosshatch patterns still limit further performance enhancement. This study demonstrates a fabrication method for fully elastically relaxed SiGe nanomembranes that effectively suppresses the formation of both threading dislocations and crosshatch patterns. The fabrication process comprises three key steps: (1) epitaxial of Si/SiGe/Si heterostructures on silicon-on-insulator (SOI) substrates via molecular beam epitaxy (MBE); (2) fabrication of periodic pore arrays using photolithography and reactive ion etching (RIE); (3) selective wet etching and subsequent transfer of nanomembranes to Si (001) substrates. Subsequently, a Si/SiGe heterostructure was grown on the SiGe nanomembranes via MBE. The full elastic relaxation state of the SiGe nanomembranes and the fully strained state of the Si quantum well in the epitaxial Si/SiGe heterostructures were verified using Raman spectroscopy. Surface root-mean-square roughness values of 0.323 nm for the SiGe nanomembrane transferred to the silicon substrate and 0.118 nm for the epitaxial Si/SiGe heterostructure were demonstrated through atomic force microscopy (AFM) measurements. Uniform surface contrast in the Si/SiGe heterostructure grown on SiGe nanomembranes was demonstrated through electron channel contrast imaging (ECCI), with no detectable threading dislocations. Comparatively, the silicon substrate region exhibits a high density of threading dislocations accompanied by stacking faults. Crosssectional transmission electron microscope (TEM) analysis shows atomically sharp and defect-free interfaces. This research establishes a critical foundation for developing high-mobility two-dimensional electron gas systems and high-performance quantum bits.