A method for producing a high quality useful layer of semiconductor material on a substrate. The method includes 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. The implanting step is conducted to minimize low-frequency roughness at the weakened zone. Next, the method includes bonding a support substrate to the face of the donor substrate, and detaching the useful layer from the donor substrate along the weakened zone. A structure is thus formed that includes the useful layer on the support substrate with the useful layer presenting a surface for further processing. The technique also includes thermally treating the structure to minimize high-frequency roughness of the surface of the useful layer. The result is a surface having sufficient smoothness so that chemical mechanical polishing (CMP) is not needed.