Theory of size effects in ferroelectric ceramic thin films on metal substrates

Abstract

The aim of this paper is to show how a Landau thermodynamic theory might be utilized to study size effects in ferroelectric thin films on metal substrates via reflectivity measurements that could be carried out with terahertz radiation, particularly in the far-infrared region. The approach taken is to minimize a Landau free energy functional that includes a gradient term to describe the size effects. Landau-Khalatnikov equations together with Maxwell’s equations for the electromagnetic field are then solved simultaneously to describe how the radiation interacts with the film. From this reflectivity curves can be calculated and related to experimental studies. Attention is paid to how the metal substrate can influence the reflectivity curves compared to free standing films without substrates. The significance of the work lies in the fact that ferroelectric ceramic thin films are becoming of increasing technological importance, and films on metal substrates such as electrodes are of obvious relevance to applications such as memory devices which rely on applied electric fields to change the polarization direction. The main conclusion is that terahertz wave measurements in the far-infrared provide an informative and sensitive probe of the size effects and substrate influence.