A method is provided for fabricating a wafer of semiconductor material intended for use for the integration of electronic and/or optical and/or optoelectronic devices. The method comprises: providing a starting wafer of crystalline silicon (205); on the starting wafer of crystalline silicon, epitaxially growing a buffer layer (210) consisting of a sub-stoichiometric alloy of silicon and germanium; epitaxially growing on the buffer layer a layer (225) of a semiconductor material having an energy gap greater than that of the crystalline silicon ...