A germanium-containing layer is deposited on a single crystalline bulk silicon substrate in an ambient including a level of oxygen partial pressure sufficient to incorporate 1%-50% of oxygen in atomic concentration. The thickness of the germanium-containing layer is preferably limited to maintain some degree of epitaxial alignment with the underlying silicon substrate. Optionally, a graded germanium-containing layer can be grown on, or replace, the germanium-containing layer. An at least partially crystalline silicon layer is subsequently deposited on the germanium-containing layer. A handle substrate is bonded to the at least partially crystalline silicon layer. The assembly of the bulk silicon substrate, the germanium-containing layer, the at least partially crystalline silicon layer, and the handle substrate is cleaved within the germanium-containing layer to provide a composite substrate including the handle substrate and the at least partially crystalline silicon layer. Any remaining germanium-containing layer on the composite substrate is removed.