Electric Field Distriutions in Dielectrics, with Special Emphasis on Near-Surface Regions in Ferroelectrics

Abstract

The characteristics of the electric field distribution due to space-charge currents in dielectric materials with both linear and nonlinear polarization are discussed, and analytic and numerical solutions for zero current are presented. In considering Poisson's equation for a material with a position-dependent polarization, we find it convenient to define a dielectric parameter in terms of the internal-electric-field derivative of the polarization rather than their quotient. In the static situation the largest electric fields exist near the surfaces for all dielectrics. Introducing the nonlinear dielectric parameter into the one-carrier model including diffusion exaggerates the effect. We expect that the strongest indications for such behavior occur in ferroelectrics since their dielectric properties are the most field sensitive. The diffusionless two-carrier recombination-center model is briefly considered. We discuss an example from the literature in terms of our "amplified-space-charge region" model and comment upon implications for device usage.