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

Abstract

In this study, analytical models for space charge limited current (SCLC) transport in a porous (or disordered) trap-limited dielectric cylindrical configuration are developed. The method used in this paper is first verified by reproducing the well-known analytical results for planar cases developed decades ago based on the traditional approach. By considering the porous solid as a fractional object characterized by a parameter α≤1, we formulate its fractional capacitance and determine the SCLC transport by using the transit time approach. At α=1, it will recover the well-known Mott–Gurney law and Mark–Helfrich 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 that 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 α extracted from such characterization can facilitate the quantitative determination of the relationship between spatial porosity and charge mobility.