Method for producing a high quality useful layer on a substrate

A method for producing a high quality useful layer of semiconductor material on a substrate, which comprises:

• implanting at least two different atomic species into a face of a donor substrate to a controlled mean implantation depth to form a weakened zone therein and to define a useful layer;
• bonding a support substrate to the face of the donor substrate;
• detaching the useful layer from the donor substrate along the weakened zone to form a structure that includes the useful layer on the support substrate with the useful layer presenting a useful layer surface for further processing, wherein the different atomic species are implanted to minimize low-frequency roughness of the useful layer surface;
• and
• thermally treating the structure to minimize high-frequency roughness of the useful layer surface to thus provide the surface having sufficient smoothness to be suitable for use in microelectronic or optoelectronic applications without conducting a chemical mechanical polishing of the useful layer surface.