Analytical model of space charge current for a cylindrical porous trap-limited dielectric

TL;DR

This paper develops an analytical model for space charge limited current in porous, trap-limited dielectrics, incorporating fractional calculus to account for porosity and providing new insights for cylindrical geometries.

Contribution

It introduces a fractional calculus-based analytical model for SCLC in porous dielectrics, extending traditional laws to cylindrical configurations with a novel fractional parameter.

Findings

Model recovers Mott Gurney and Helfrich laws at a=1

Provides analytical form for cylindrical geometry

Facilitates characterization of porosity effects in SCLC

Abstract

In this study, analytical models for space charge limited current (SCLC) transport in a porous (or disordered) trap-limited dielectric are derived for both planar and cylindrical configuration. By considering the porous solid as a fractional object characterized by a parameter a less than 1, we formulate its fractional capacitance and determine the SCLC transport by using the transit time approach. At a equal to 1, it will recover the well-known Mott Gurney (MG) law and Mark Helfrich (MH) law for trap-free and trap-limited cases, respectively. For cylindrical geometry, our findings show an analytical form that is not available from the traditional methods. We anticipate the proposed analytical model will serve as a useful tool for characterizing the current-voltage measurements in SCLC transport in dielectric breakdown and organic electronics, where spatial porosity of the materials is inevitable. The introduced fractional parameter a extracted from such characterization can facilitate the quantitative determination of the relationship between spatial porosity and charge mobility.