The invention relates to a process for fabricating a heterostructure comprising at least one thin layer and a carrier substrate made of a semiconductor, the process comprising: bonding a first substrate made of a single-crystal first material, the first substrate comprising a superficial layer made of a polycrystalline second material, to a second substrate so that a bonding interface is created between the polycrystalline layer and the second substrate; removing from the free surface of one of the substrates, called the donor substrate, a thickness thereof so that only a thin layer is preserved; generating a layer of amorphous semiconductor material between the first substrate and the bonding interface by amorphization of the layer of polycrystalline material; and crystallizing the layer of amorphous semiconductor material, the newly crystallized layer having the same orientation as the adjacent first substrate.