Continuum modeling of charged vacancy migration in elastic dielectric solids, with application to perovskite thin films

A continuum theory describing the behavior of dielectric materials containing mobile, electrically charged vacancies is formulated. The theory is implemented to simulate diffusion, at the nanometer scale, of oxygen vacancies in acceptor-doped barium strontium titanate (BST) thin films in the paraelectric state. In the simulations, charged vacancies coalesce into boundary layers of large concentration at potential-free interfaces, with increases in the local electric field intensity emerging near such boundaries. Upon relating this increase to a reduction in the energy barrier for charge transmission from film to electrode at the interface, and accepting an inverse relationship between the concentrations of doping elements and mobile oxygen vacancies, the model shows agreement with observed trends of decreasing current losses with increased doping.