A method of fabricating a hybrid substrate by direct bonding of donor and receiver substrates where each substrate has a respective front face and surface, with the front face of the receiver substrate having a semiconductor material near the surface, and the donor substrate including a zone of weakness that defines a layer to be transferred. The method includes preparing the substrate surfaces by exposing the surface of the receiver substrate to a temperature from about 900° C. to about 1200° C. in an inert atmosphere for at least 30 sec; directly bonding together the front faces of the prepared substrates to form a composite substrate; heat treating the composite substrate to increase bonding strength between the front surfaces of the donor and receiver substrates; and transferring the layer from the donor substrate by detaching the remainder of the donor substrate at the zone of weakness.