Silicon-based single-crystal portions are produced on a surface of a substrate, selectively in zones where a single-crystal material is initially exposed. To do this, a layer is firstly formed over the entire surface of the substrate, using a silicon precursor of the non-chlorinated hydride type, and under suitable conditions so that the layer is a single-crystal layer in the zones of the substrate where a single-crystal material is initially exposed and amorphous outside these zones. The amorphous portions of the layer are then selectively etched so that only the single-crystal portions of the layer remain on the substrate.