  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.
