A method of fabricating a semiconductor substrate includes the following activities: a) providing a donor substrate with a weakened zone inside the donor substrate, the weakened zone forming a border between a layer to be transferred and the rest of the donor substrate, b) attaching the donor substrate to a receiver substrate, the layer to be transferred being located at the interface between the donor substrate and the receiver substrate; c) detaching the receiver substrate along with the transferred layer from the rest of the donor substrate, at the weakened zone; and d) at least one step of smoothing the surface of the transferred layer, wherein the semiconductor substrate obtained from step c) is kept, at least from the moment of detachment until the end of the smoothing step, in a non-oxidizing inert atmosphere or in a mixture of non-oxidizing inert gases. Semiconductor substrates are fabricated using such a method.