The invention specifically relates to methods of fabricating a composite substrate by providing a first insulating layer on a support substrate at a thickness of e.sub.1 and providing a second insulating layer on a source substrate at a thickness of e.sub.2, with each layer having an exposed face for bonding; providing plasma activation energy in an amount sufficient to activate a portion of the thickness of the face of the first insulating layer e.sub.mp1 and a portion of the thickness of the face of the second insulating layer e.sub.mp1; providing a final insulating layer by molecular bonding the activated face of the first insulating layer with the activated face of the second insulating layer; and removing a back portion of the source substrate while retaining an active layer comprising a remaining portion of the source substrate bonded to the support substrate with the final insulating layer interposed therein to form the composite substrate. The thicknesses e.sub.1, e.sub.2 of the first and second insulating layers are sufficient to provide the final insulating layer with a thickness of 50 nanometers or less, and the plasma activation energy and respective thicknesses e.sub.1, e.sub.2 of the first and second insulating layers are selected such that only respective thicknesses e.sub.mp1 and e.sub.mp2 of the faces of the first insulating layer and the second insulating layer are activated.