Effect of injection barrier height on charge transport under bipolar injection

Abstract

In this paper, a numerical model describing the transient phenomena of electric charge in a dielectric because of a double injection at 2 electrodes is proposed. The mathematical model and the methods for its resolution are presented step by step. Thus, the Schottky equation is used to describe the injection of negative and positive charges from the cathode and anode respectively. The equations governing the conduction are the current equation and the Poisson equation coupled to the continuity equation. The adopted model uses the applied voltage instead of the applied electric field. The Poisson equation is solved by finite differences using the Thomas algorithm and the continuity equation by Euler's method. The Thomas algorithm reduces considerably the execution time compared to iterative methods. The time step is not constant; it is calculated from the speed of the charges front. The results show that the established model and the method of resolution reproduce correctly the behaviour of the system under a high voltage.It shows also that knowing the injection barrier height can be used to predict the behaviour of the dielectric under electrical stress. The developed model is a tool for describing the behaviour of the charges for a bipolar injection.

An Efficient Numerical Technique for the Simulation of Charge Transport in Polymeric Dielectrics

“…For example, in [22], [23], [24] the finite element method (FEM) was used for spatial discretization, coupled with a Runge-Kutta time integration scheme. Meftali et al focused on the effect of the injection barrier height on the results of the bipolar transport model using finite differences and an explicit time integrator [25]. Recently, Doedens et al proposed a comprehensive model to describe the effect of electrodes surface roughness on the space charge accumulation phenomenon inside XLPE [26], [27].…”