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Self-compensation, the tendency of a crystal to lower its energy by forming point defects to counter the effects of a dopant, is here quantitatively proven. Based on a new theoretical formalism and several different experimental techniques, we demonstrate that the addition of 1.4 × 1021-cm−3 Ga donors in ZnO causes the lattice to form 1.7 × 1020-cm−3 Zn-vacancy acceptors. The calculated VZn formation energy of 0.2 eV is consistent with predictions from density functional theory. Our formalism is of general validity and can be used to investigate self-compensation in any degenerate semiconductor material.Peer reviewe

Self-compensation in semiconductors: The Zn vacancy in Ga-doped ZnO