A single crystal germanium-on-silicon structure includes a single crystal silicon substrate. A single crystal layer of gadolinium oxide is epitaxially grown on the substrate. The gadolinium oxide has a cubic crystal structure and a lattice spacing approximately equal to the lattice spacing or a multiple of the single crystal silicon. A single crystal layer of lanthanum oxide is epitaxially grown on the gadolinium oxide with a thickness of approximately 12 nm or less. The lanthanum oxide has a lattice spacing approximately equal to the lattice spacing or a multiple of single crystal germanium and a cubic crystal structure approximately similar to the cubic crystal structure of the gadolinium oxide. A single crystal layer of germanium with a (111) crystal orientation is epitaxially grown on the layer of lanthanum oxide.