A method for transferring a layer of semiconductor material from a wafer is described. The wafer includes a support substrate and an upper surface that includes a buffer layer of a material having a first lattice parameter. In an embodiment, the technique includes growing a strained layer on the buffer layer. The strained layer is made of a semiconductor material having a nominal lattice parameter that is substantially different from the first lattice parameter, and it is grown to a thickness that is sufficiently thin to avoid relaxation of the strain therein. The method also includes growing a relaxed layer on the strained layer. The relaxed layer is made of silicon and has a concentration of at least one other semiconductor material that has a nominal lattice parameter that is substantially identical to the first lattice parameter. The technique also includes providing a weakened zone in the buffer layer, and supplying energy to detach a structure at the weakened zone. The structure includes a portion of the buffer layer, the strained layer and the relaxed layer. Lastly; the method includes enriching the concentration of the at least one other semiconductor material in the relaxed layer of the structure.