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

Abstract

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 \ifmmode\times\else\texttimes\fi{} 10${}^{21}$-cm${}^{\ensuremath{-}3}$ Ga donors in ZnO causes the lattice to form 1.7 \ifmmode\times\else\texttimes\fi{} 10${}^{20}$-cm${}^{\ensuremath{-}3}$ Zn-vacancy acceptors. The calculated ${V}_{\mathrm{Zn}}$ 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.