Self-compensation, the tendency of a crystal to lower its energy by forming point defects to counter the effects of a dopant, was here quantitatively proven. Based on a new theoretical formalism and several different experimental techniques, it was demonstrated that the addition of 1.4 x 1021/cm3 Ga donors in ZnO caused the lattice to form 1.7 x 1020/cm3 Zn-vacancy acceptors. The calculated VZn formation energy of 0.2eV was consistent with predictions from density functional theory. This formalism was of general validity and could be used to investigate self-compensation in any degenerate semiconductor material.

Self-Compensation in Semiconductors: the Zn Vacancy in Ga-Doped ZnO. Look, D.C., Leedy, K.D., Vines, L., Svensson, B.G., Zubiaga, A., Tuomisto, F., Doutt, D.R., Brillson, L.J.: Physica Review B, 2011, 84[11], 115202