Simulation of bipolar charge transport in polyethylene featuring trapping and hopping conduction through an exponential distribution of traps

We present an asymmetric bipolar model of conduction intended to describe temporal and spatial evolution of space charge density and external current in cross-linked polyethylene under a uniform applied DC field. Carriers of both polarities are provided by injection at the electrodes according to the Schottky law. Charge transport is described by a hopping mechanism in which carriers move from site to site by getting over a potential barrier. An exponential distribution of trap levels with a maximum limit in trap depth is adopted for the model. Net charge density profiles and external current are obtained by solving the continuity equation for electrons and holes and the Poisson equation for electric field coupled to transport equation. The aim of this work is to use the simulations to evaluate the influence of temperature and applied field on the net charge density profiles.