Application of tensile strain to the Si(100) lattice is known to enhance carrier mobility in field effect transistors through modification of the Si band structure. Si is conventionally placed under tensile strain using methods such as Si3N4 capping for strained channel devices, and epitaxial growth of Si on a strain graded SiGe substrate for large area strain. The latter case preserves and propagates threading dislocations, and both cases require use of a bulk rigid substrate, which prohibits the use of strained Si in applications such as flexible electronics, or indeed in any application where strained Si is desirable on a non-epitaxial substrate. Elastically strained, single-crystal, Si-based nanomembranes, in which the release of a Si/SiGe/Si heterostructure from its growth substrate allows elastic strain sharing between the layers, circumvent these issues. These nanomembranes are extremely flexible, virtually dislocation-free, and transferable to almost any other surface.