A method of forming a low-defect, substantially relaxed SiGe-on-insulator substrate material is provided. The method includes first forming a Ge-containing layer on a surface of a first single crystal Si layer which is present atop a barrier layer that is resistant to Ge diffusion. A heating step is then performed at a temperature that approaches the melting point of the final SiGe alloy and retards the formation of stacking fault defects while retaining Ge. The heating step permits interdiffusion of Ge throughout the first single crystal Si layer and the Ge-containing layer thereby forming a substantially relaxed, single crystal SiGe layer atop the barrier layer. Moreover, because the heating step is carried out at a temperature that approaches the melting point of the final SiGe alloy, defects that persist in the single crystal SiGe layer as a result of relaxation are efficiently annihilated therefrom.