A system and method for producing a single-crystal germanium layer on a dielectric layer by producing a germanium-on-insulator assembly between the surface portions of the third material. The choice of location for these surface portions therefore makes it possible to define the zone on which it is desired to produce the germanium-on-insulator layer. The wafer may be freely chosen between a pure single-crystal silicon wafer and a silicon-on-insulator wafer. A single-crystal germanium first layer is produced on the surface portion of the silicon. The RPCVD produces a partially crystalline germanium first layer. The layer thus comprises various nuclei that have crystallized in possibly different lattices. After carrying out a recrystallization annealing operation, which makes the layer monocrystalline by recrystallizing the various nuclei in one and the same crystal lattice. Thus, the layers are continuous with the single-crystal silicon lattice.