SiGe/Si quantum wells are of great interest for the development of Group-IV THz quantum cascade lasers. The main advantage of Group-IV over III-V materials such as GaAs is that, In the former, polar phonon scattering, which significantly diminishes the efficiency of intersubband light emission, is absent. However, for SiGe/SI multiple-quantum-well structures grown on bulk Si, the lattice mismatch between Si and Ge limits the critical thickness for dislocation formation and thus the number of periods that can be grown. Similarly, the use of composition-graded SiGe films as a lattice-matched substrate leads to the transfer of dislocations from the graded buffer substrate into the quantum wells, with a consequent decrease in light emission efficiency. Here we Instead employ nanomembrane strain engineering to fabricate dislocation-free strain relaxed substrates, with lattice constants that match the average lattice constants of the quantum wells. This procedure allows for the growth of many periods with excellent structural properties. The samples in this work were grown by low-pressure chemical vapor deposition and characterized via high-resolution X-ray diffraction and far-infrared transmission spectroscopy, showing narrow intersubband absorption features indicative of high crystalline quality.