Theoretical study of Fe doping and oxidation–reduction influence on the photorefractive effect in BaTiO_3

We numerically solve charge-transport and Poisson equations for photorefractive BaTiO3 single crystals with a band model, using four impurity levels, Fe2+–Fe3+, Fe3+–Fe4+, VO••–VO•, and VO•-VOx. Densities and photoinduced spatial distributions of each population are computed as a function of annealing O partial pressure. Space-charge field and beam-coupling gain are also computed as a function of annealing O partial pressure, temperature, Fe concentration, grating wave vector, and light intensity. We discuss the intervening mechanism of impurity centers and the correlations between experimental conditions of crystal growth, oxidation–reduction treatments, and measurement parameters.