Bipolar charge transport model with trapping and recombination: an analysis of the current versus applied electric field characteristic in steady state conditions

A bipolar model of transport intended to describe the behaviour of polyethylene under dc stress in steady state conditions is presented. The model is based on Poisson's equation and the conservation law of charges, with trapping, detrapping and recombination phenomena being taken into account. Electric field and carrier concentrations are formulated for double-carrier injection and boundary conditions are given by the Schottky injection law. This system of equations with partial differential functions is solved using a finite volume method. The current versus applied electric field characteristic is obtained and analysed for different parameter sets of the model in order to understand their role in the predicted macroscopic behaviour. To do so, we consider two approaches. In a first step, the simulation has been realized with symmetric parameters for positive and negative charge carriers in order to facilitate the interpretation. In a second step, asymmetric parameters have been considered in the model as it constitutes a more realistic situation. Results show that the recombination plays an essential role in order to obtain the two changes in slope, forming a sigmoid-like shape in the current-voltage characteristic as observed experimentally in this kind of material.