Interaction of oxygen vacancies with domain walls and its impact on fatigue in ferroelectric thin films

The role of oxygen vacancies in fatigue and dielectric breakdown has been a topic of intense research in ferroelectric perovskites like BaTiO_3. This paper presents a comprehensive model that treats the ferroelectrics as polarizable wide band-gap semiconductors where the oxygen vacancies act as donors. First, a fully coupled nonlinear model is developed with space charges, polarization, electric potential and elastic displacements as variables without making any a priori assumptions on the space charge distribution and the polarization. Second, a Pt/BaTiO_3/Pt structure is considered. Full-field coupled numerical simulations are used to investigate the structure of 180° and 90° domain walls in both perfect and defected crystals. The interactions of oxygen vacancies with domain walls are explored. Numerical results show that there is pronounced charge trapping near 90° domain walls, giving rise to possible domain wall pinning and dielectric breakdown. Third, a simple analytical solution of the potential profile for a metal/ferroelectric semiconductor interface is obtained and the depletion layer width is estimated. These analytical estimates agree with our numerical results and provide a useful tool to discuss the implications of our results.