Properties of species profiles during oxygen chemical diffusion in oxides

The profiles of species during the oxygen chemical diffusion in an acceptor doped oxide crystal driven by large changes in the ambient oxygen partial pressure are studied theoretically. The oxide crystal containing forth species (mobile oxygen vacancy, mobile electron, two states of immobile dopant ion) and taking into account one internal reaction (valence transformation of the dopant ion) is considered. Our analysis is based on the expression of the ambipolar chemical diffusion coefficient obtained in the framework of the concept of conservative ensembles (Maier J., 1993). It is assumed that the equilibrium constant of the internal reaction is much smaller than the acceptor dopant concentration. This condition is fulfilled in many wide band gap oxide crystals. It is shown that the dependence of chemical diffusion coefficient on ambient oxygen partial pressure on logarithmic scale is divided to the distinct intervals. The chemical diffusion equation is reduced inside intervals to the diffusion equation with a diffusion coefficient which depends on concentration by power law. At changing of the ambient oxygen partial pressure inside the intervals two singularities on the species diffusion profiles are found: an internal reaction diffusion front during reduction and an ambipolar diffusion front during oxidation. The ambipolar diffusion front has a shape of the electron concentration step moving into specimen. The generalization of the obtained results on large number species and reactions is discussed.