Theory of doping properties of Ag acceptors in ZnO

Doping properties of Ag in ZnO were analyzed by first-principles calculations within both the local-density and generalized gradient approximations. The ionization energy of ${\text{Ag}}_{\text{Zn}}$, about 0.2 eV, is comparable to that of the commonly used group-V acceptors, and is lower than that of two other ${\text{I}}^{\text{B}}$ species, Cu and Au. Formation energy of Ag in the favorable O-rich conditions is 0.85 eV, which corresponds to the solubility limit of about ${10}^{18}\text{ }{\text{cm}}^{\ensuremath{-}3}$ at $700\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$. Formation of Ag-rich second phases is predicted for high Ag concentrations. Energetics of the onset of this process is analyzed and ${\text{Ag}}_{\text{Zn}}$ display a tendency to form aggregates of AgO with the wurtzite structure. Formation of such nanoinclusions is shown to affect the lattice constant of ZnO:Ag. Two ``wrong'' incorporation channels, i.e., at the interstitial sites and at the oxygen sites as ${\text{Ag}}_{\text{O}}$, are predicted to be nonefficient due to the high formation energies. The calculated magnetic coupling between Ag ion reveals an unexpected dependence on the Ag-Ag distance; the interaction between the nearest-neighbor ${\text{Ag}}_{\text{Zn}}$ pair vanishes while that for the more distant pairs is weakly ferromagnetic.