We compare the morphological and structural features of SiGe membranes fabricated by three different processes: direct deposition of Si0.5Ge0.5 on. Si(001) nominal substrate, direct deposition Of Si0.5Ge0.5 on silicon on insulator, and deposition of SiGe with low Ge concentration on silicon on insulator followed by Ge enrichment by condensation. We show that the formation of fully strained Ge-rich layers free of defects with a flat surface is possible only by the two-step epitaxy-condensation process. We demonstrate that the condensation based process enables the total inhibition of the morphological instability, together with the hindering of dislocations for critical thickness much greater than those commonly obtained by direct deposition. Those behaviors could be explained by the injection of self-interstitials in the Ge-rich layers during condensation. Such remarkable properties systems using a similar condensation process. could be generalized to many other systems using a similar condensation process.