Electrostatic conductive disc singularity resolved

Abstract

The conventional electrostatic solutions for two-dimensional (2D) electrodes possess edge singularities for the surface charge density σ and the normal component of the electric field En. These singularities are generally non-physical because they admit infinite gradients of the concentration of free charge carriers. In particular, they are unacceptable in the studies of the local field sensitive effects, such as the electric breakdown and the ferroelectric domain reversal. We claim that account for diffusion of free charge carriers leads to the disappearance of the edge singularities. This generalization occurs consistently within the same basic concept of conduction. Specifically, we consider the case of U-biased circular disc electrode of radius a. Account for diffusion leads here to a strongly nonlinear integral 2D equation for the electrostatic potential φ(r). Numerical solution of this equation shows that the law σ(a)∝U2/a takes place. Outside a close vicinity of the disc edge, we stay close to the conventional electrostatic solution for φ and σ.