SOI wafers are manufactured by forming on a silicon substrate a monocrystalline first, cubic 1a-3 metal or mixed metal oxide layer whose lattice constant differs from that of the substrate by 5% or less; forming a second cubic 1a-3 mixed metal oxide layer having a lattice constant within 2% of the lattice constant of the first metal or mixed metal oxide layer, and having a graded metal content to vary the lattice content in the second mixed metal oxide layer from that of the first layer, and thermally treating the layered product in an oxygen atmosphere to form an amorphous interlayer between the substrate and the first metal or mixed metal oxide layer.