Effect of Zinc Vacancy on Carrier Concentrations of Nonstoichiometric ZnO

We proposed that concentrations of cartier electron as well as ionized donor defects in nonstoichiometric ZnO are proportional to $P^{-1/2}_{O_2}$, whenever they ionizes singly or doubly, by employing the Fermi-Dirac (FD) statistics for ionization of the native thermal defects $Zn_i$ and $V_o$. The effect of acceptor defect, zinc vacancy $V_{Zn}$made by the Frenkel and Schottky disorder reactions, on carrier concentrations was discussed. By application of the FD statistics law to their ionization while the formation of defects is assumed governed by the mass-action law, the calculation results indicate; 1. ZnO shows n-type conductivity with $N_D>$N_A$ and majority concentration of $n{\propto}\;P^{-1/2}_{O_2}$ in a range of $P_{O_2}$, lower than a critical value. 2. As the concentration of acceptor $V_{Zn}$ increases proportional to $P^{1/2}_{O_{2}}$, ZnO made at extremely high $P_{O_{2}}$, can have p-type conductivity with majority concentration of p ${\propto}\;P^{-1/2}_{O_{2}}$. One may not, however, obtain p-type ZnO if the pressure for $N_{D}<$N_{A}$ is too high.