A method of forming a relaxed SiGe-on-insulator substrate having enhanced relaxation, significantly lower defect density and improved surface quality is provided. The method includes forming a SiGe alloy layer on a surface of a first single crystal Si layer. The first single crystal Si layer has an interface with an underlying barrier layer that is resistant to Ge diffusion. Next, ions that are capable of forming defects that allow mechanical decoupling at or near said interface are implanted into the structure and thereafter the structure including the implanted ions is subjected to a heating step which permits interdiffusion of Ge throughout the first single crystal Si layer and the SiGe layer to form a substantially relaxed, single crystal and homogeneous SiGe layer atop the barrier layer. SiGe-on-insulator substrates having the improved properties as well as heterostructures containing the same are also provided.