Abstract: Disclosed is a method for the growing of heteroepitaxial layers of monocrystalline semiconductor materials. To this end, on a substrate made of a material of a first type, there is made a seed of a second type of material. This seed is between a face of the substrate and a confinement layer which defines a confinement space with the face of the substrate. A vapor phase epitaxy of a material of the second type is then effected in the confinement space. This material of the second type grows from the seed in the confinement space. The method can be applied to the manufacture of heterogeneous semiconductor structures and to the three-dimensional integration of semiconductor components.