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In this study, analytical models for space charge limited current (SCLC)transport in a porous (or disordered) trap-limited dielectric are derived forboth planar and cylindrical configuration. By considering the porous solid as afractional object characterized by a parameter a less than 1, we formulate itsfractional capacitance and determine the SCLC transport by using the transittime 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 formthat is not available from the traditional methods. We anticipate the proposedanalytical model will serve as a useful tool for characterizing thecurrent-voltage measurements in SCLC transport in dielectric breakdown andorganic electronics, where spatial porosity of the materials is inevitable. Theintroduced fractional parameter a extracted from such characterization canfacilitate the quantitative determination of the relationship between spatialporosity and charge mobility.

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