Charge injection instability in perfect insulators

TL;DR

This paper investigates charge injection instabilities in perfect insulators, revealing how localized charge formation and slow redistribution lead to bistability and are influenced by defect geometry and nonlinear mobility.

Contribution

It introduces a model explaining charge injection instability and bistability in perfect insulators, highlighting the role of defect geometry and nonlinear carrier mobility.

Findings

Charge injection leads to localized charge clouds near defects.

The formation of the charged state involves two distinct time scales.

The model explains the increase of critical electric field with smaller contact size.

Abstract

We show that in a macroscopic perfect insulator, charge injection at a field-enhancing defect is associated with an instability of the insulating state or with bistability of the insulating and the charged state. The effect of a nonlinear carrier mobility is emphasized. The formation of the charged state is governed by two different processes with clearly separated time scales. First, due to a fast growth of a charge-injection mode, a localized charge cloud forms near the injecting defect (or contact). Charge injection stops when the field enhancement is screened below criticality. Secondly, the charge slowly redistributes in the bulk. The linear instability mechanism and the final charged steady state are discussed for a simple model and for cylindrical and spherical geometries. The theory explains an experimentally observed increase of the critical electric field with decreasing size of the injecting contact. Numerical results are presented for dc and ac biased insulators.