TY - JOUR

T1 - Electrostatic conductive disc singularity resolved

AU - Smirnov, S.

AU - Podivilov, E.

AU - Sturman, B.

PY - 2024/3

Y1 - 2024/3

N2 - 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 E n . 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 ) ∝ U 2 / a takes place. Outside a close vicinity of the disc edge, we stay close to the conventional electrostatic solution for φ and σ .

AB - 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 E n . 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 ) ∝ U 2 / a takes place. Outside a close vicinity of the disc edge, we stay close to the conventional electrostatic solution for φ and σ .

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85189081944&origin=inward&txGid=4a1903d3e324a4e1cbdf930efc7ea700

UR - https://www.mendeley.com/catalogue/99ebaceb-ebc5-3029-8aa5-ec123e1ee391/

U2 - 10.1063/5.0190593

DO - 10.1063/5.0190593

M3 - Article

VL - 135

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 12

M1 - 124301

ER -