Numerical simulation of the effects of space charge and Schottky barrier on ferroelectric thin films

The roles of space charge induced by oxygen vacancies and the Schottky barrier due to the electrode/film heterojunction are investigated numerically using Landau-Khalatnikov theory. In this model, the thin film is considered as the stacking of dipolar layers along the thickness direction. The free energy for each layer obeys the well-known double-well p⁴ model. By solving the one-dimensional Poisson equation, the non-uniform electric field is determined by the boundary condition imposed by the Schottky barrier as well as the space charge distribution inside the film. It is revealed that the asymmetric hysteresis p-E loop is the consequence of the unequal Schottky barriers at the two electrode/film interfaces. Moreover, the space charge distribution results in the distorted hysteresis loop. Both phenomena are detrimental effects for ferroelectric memory