Model for ferroelectric semiconductors thin films accounting for the space varying permittivity

Abstract

Reducing thickness of ferroelectric films typically comes with an apparent degradation of their ferroelectric and dielectric properties. The existence of low-dielectric interfacial layers is often invoked to explain such behaviors. Much work has been done on modeling ferroelectric thin films by considering a ferroelectric layer between two layers with low dielectric constant. In these models it is necessary to introduce extrinsic parameters; the dielectric constant and the polarization are step functions of the depth inside the film. We have developed a model for ferroelectric semiconductors based on the inhomogeneous Landau–Devonshire theory, including surface effects. The local electric field is determined by solving Poisson’s equation in which a differential permittivity replaces the dielectric constant. We have found that the hysteresis loops were strongly influenced by the correlation length. That point is discussed by examining the electric field, polarization, and differential permittivity profile inside the film. It is shown that the differential permittivity strongly decreases with the correlation length increases. That phenomena leads to high electric fields inside the film and especially close to the surface. As a consequence, an explanation for thin film ferroelectric properties can be given by invoking space charge density many orders of magnitude lower than those usually considered.