Compressive strain semiconductor substrates

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A method for forming a compressively strained semiconductor substrate includes forming a lattice adjustment layer on a semiconductor substrate by forming compound clusters within an epitaxially grown semiconductor matrix. The lattice adjustment layer includes a different lattice constant than the semiconductor substrate. A rare earth oxide is grown and lattice matched to the lattice adjustment layer. A semiconductor layer is grown and lattice matched to the rare earth oxide and includes a same material as the semiconductor substrate such that the semiconductor layer is compressively strained.