Determination of the Gibbs free energy of formation of Ga vacancies in GaAs by positron annihilation

We determined the Gibbs free energy of formation—i.e., the formation enthalpy and entropy—as well as the charge state of Ga vacancies in n-type GaAs by directly probing the vacancy concentration as a function of annealing temperature, arsenic vapor pressure, and doping concentration using positron annihilation. The Ga vacancy concentration increases with doping concentration and arsenic vapor pressure, but decreases with temperature. Using equilibrium thermodynamics, we obtained a $-3e$ charge state of the Ga vacancy in n-doped GaAs as well as a formation enthalpy of $(3.2\mathrm{}\pm 0.5)\mathrm{eV}$ and a formation entropy of $(9.6\mathrm{}\pm {1)k}_B$ for the uncharged vacancy state.