A method for manufacturing a structured substrate provided with a trap-rich layer whereon rests a stack consisting of an insulating layer and of a layer of single-crystal material, includes forming an amorphous silicon layer on a front face of a silicon substrate and heat treating intended to convert the amorphous silicon layer into a trap-rich layer made of single-crystal silicon grains. The heat treatment conditions in terms of duration and of temperature are adjusted to limit the grains to a size less than 200 nm. The method also includes overlapping the trap-rich layer with an insulating layer and a layer of single-crystal material.