Distribution of oxygen vacancies in an external electric field and oxygen-ion conductivity in acceptor-doped fluorite-structured ionic conductors

The charge carrier distribution across lattice sites of fluorite-structured oxides of the type (AO$_2$)$_{1-x}$(BO$_{1.5}$)$_{x}$ is calculated in the region of not quite high dopant concentrations in an external electric field by solving the master equation under the assumption of steady state. The effect that redistribution of ions in the external electric field has on the value for ionic conductivity and the position of the maximum in its dependence on the impurity content is investigated. The conductivity is treated within a model in which the effect of impurity on the carrier transport reduces itself to blockage of charge carrier jumps along edges of the oxygen lattice that are closest to doping ions. The results of analytical calculations are corroborated by numerical Monte Carlo modeling and can be used to treat the position of maxima in experimental dependences of conductivity on the dopant concentration in similar structures.