Geometry dependence of 2-dimensional space-charge-limited currents

TL;DR

This paper develops an analytical theory describing how the geometry of electrodes influences space-charge-limited currents in thin films, highlighting conditions for current sustainability based on field singularities.

Contribution

It introduces a largely analytical framework for understanding geometry effects on space-charge-limited currents in zero-thickness films, including criteria for current sustainability.

Findings

Current can only be sustained if electrode-induced field singularities meet specific conditions.

Certain geometries prevent space-charge-limited current in zero-thickness models, requiring thickness considerations.

Numerical models are necessary when zero-thickness assumptions fail due to geometry.

Abstract

The space-charge-limited current in a zero thickness planar thin film depends on the geometry of the electrodes. We present a theory which is to a large extent analytical and applicable to many different lay-outs. We show that a space-charge-limited current can only be sustained if the emitting electrode induces a singularity in the field and if the singularity induced by the collecting electrode is not too strong. For those lay-outs where no space-charge-limited current can be sustained for a zero thickness film, the real thickness of the film must be taken into account using a numerical model.