The formation of equilibrium space-charge zones at grain boundaries in the perovskite oxide SrTiO₃

The thermodynamics of space-charge formation at grain boundaries in acceptor-doped SrTiO₃ is examined. Thermodynamic models of varying complexity are developed, which predict the space-charge potential as a function of thermodynamic variables, such as dopant concentration, temperature and oxygen partial pressure. Based on the results, limits to the space-charge potential that can arise at a grain boundary and strategies for tuning the space-charge potential are discussed. With literature equations linking the space-charge potential to electrical properties, one specific thermodynamic model is subsequently applied to electrical impedance data reported in the literature for tilt bicrystal samples of Fe-doped SrTiO₃. The thermodynamic driving energies for space-charge formation obtained from the analysis are examined as a function of tilt misorientation angle, in order to explore the relationship between driving energy and interface atomistic structure. In addition, the capabilities and deficiencies of the entire approach (from driving energies via space-charge potentials to electrical properties), with regard to predicting experimental behaviour, are demonstrated.