A method of producing a very large area germanium layer on a silicon substrate, comprises forming an initial layer of germanium on the silicon substrate such that rounded S—K protuberances are produced by lattice mismatch. Oxidation produces silicon dioxide between the protuberances, and a subsequent reduction step exposes the tops of the protuberances. Since the top regions are almost perfectly relaxed and free of stress, these form nucleation sites for the subsequent growth of a final layer of germanium, formed as single crystals each extending from a nucleation site.