Modeling charge transport and linking charge dynamics with dissipative processes responsible for electrical ageing are a challenging objective for developing a mature approach in insulation design. Such an approach is exemplified here for polyethylenebased materials by introducing two models describing bipolar Space Charge Limited Current in transient and steady states. They rely on two classical descriptions of the distribution function of the energy levels of trap states -single trapping level or exponential distribution. Their predictions are discussed as regards the experimental behavior. They notably highlight the importance of recombination processes in explaining the sigmoidal shape of the steady-state current-voltage characteristic. Also, bipolar charge transport seems to be a necessary factor for the observed features of oscillatory charge packets. The energetic features of charge dynamics is reviewed with particular emphasis on recombination phenomena because the latter promote electronically excited states that are chemically reactive and could be involved in ageing reaction. The relationship between charge recombination and electroluminescence is highlighted through experiments and simulation. The spectral analysis of the emitted light advocates the existence of massive chemical/physical degradation in the electrical regime where recombination is a major factor of the Space Charge Limited Current (SCLC).

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.

A charge transport model allowing the description of electroluminescence in polyethylene films under AC stress is proposed. The fluid model incorporates bi-polar charge injection/extraction, transport and recombination. The physics is based on hopping-mobility of electronic carriers between traps with an exponential distribution in which trap-filling controls the mobility. The computation mesh is very tight close to the electrodes-of the order of 0.4 nm allowing mapping the density of positive and negative carriers during sinusoidal, triangular and square 50 Hz voltage waveforms. Experiment and simulation fit nicely and the time-dependence of the electroluminescence intensity is accounted for by the charge behaviour. Light emission scales with the injection current. It is shown that space charge affects a layer of 10 nm away from the electrode where the mobility is increased as compared to the bulk mobility due to the high density of charge. The approach is very encouraging and opens the way to model space charge under timevarying voltages.

A sixth-order finite volume method is proposed to solve the Poisson equation for two-and three-dimensional geometries involving curved boundaries. A specific polynomial reconstruction is used to provide accurate fluxes for diffusive operators even with discontinuous coefficients while we introduce a new technique to preserve the sixth-order approximation for non-polygonal domains. Numerical tests covering a large panel of situations are addressed to assess the performances of the method.

This paper proposes a numerical model for describing charge accumulation in electron-beam irradiated low density polyethylene. The model is bipolar, and based on a previous model dedicated to space charge accumulation in solid dielectrics under electrical stress. It encompasses the generation of positive and negative charges due to the electron beam and their transport in the insulation. A sensitivity analysis of the model to parameters specific to electron beam irradiation is performed in order to understand the impact of each process on the space charge distribution. At last, a direct comparison between time dependent space charge distribution issued from the model and from measurements is performed. The transport parameters used for the simulations are the same as those optimized for transportation in polyethylene under an external electric field giving a robustness in the modelling approach because of the constrains on fitting parameters that must comply to a set of experimental results.PACS Numbers: 72.20Ht, 72.20Jv 1. Introduction Solid dielectrics used as thermal blanket on geostationary satellites are submitted to the flow of several types of charged particles, and particularly to electrons. These materials can accumulate charges, building up the potential inside the dielectric, meaning a potential difference between different parts of the satellite. Electrostatic Surface Discharge (ESD) can occur, leading to possible damages of the electronics of the satellite [1]. In order to prevent such ESD to happen, it is necessary to understand the dynamics of the charge transport in solid dielectrics used in space environment. A number of studies have been carried out in this domain. Some are experimental, measuring the surface potential of the irradiated samples, the current flow during irradiation [2] and the space charge distribution after irradiation [3]. Recently, two original set-ups [4-5] to measure space charge distribution in electronbeam irradiated samples have been developed on the basis of the Pulsed Electro-Acoustic (PEA) method. With these experimental tools, it is now possible to observe the dynamic of charging and discharging in electron-beam irradiated materials. On the other hand, a number of works on theoretical background and simulation has been done in order to understand and reproduce the behaviour of charge in electron beam irradiated polymers [6][7][8][9]. Our very aim is to develop space charge modelling in electron beam irradiated materials in nonstationary conditions through an approach that closely associates experiment and numerical simulation. Within the first part of this paper, we briefly review the state-of-the-art on modelling charge transport in synthetic insulations under electron beam irradiation in order to establish the position of our approach. Then, we describe the proposed model, which has been adapted from a previous one [10] developed for space charge conduction in a Low Density Polyethylene (LDPE) under DC stress. The same set of transport parameters has b...

Articles you may be interested inNumerical simulations of electrostatic interactions between an atomic force microscopy tip and a dielectric sample in presence of buried nano-particles Electric Force-Distance Curves (EFDC) is one of the ways whereby electrical charges trapped at the surface of dielectric materials can be probed. To reach a quantitative analysis of stored charge quantities, measurements using an Atomic Force Microscope (AFM) must go with an appropriate simulation of electrostatic forces at play in the method. This is the objective of this work, where simulation results for the electrostatic force between an AFM sensor and the dielectric surface are presented for different bias voltages on the tip. The aim is to analyse force-distance curves modification induced by electrostatic charges. The sensor is composed by a cantilever supporting a pyramidal tip terminated by a spherical apex. The contribution to force from cantilever is neglected here. A model of force curve has been developed using the Finite Volume Method. The scheme is based on the Polynomial Reconstruction Operator-PRO-scheme. First results of the computation of electrostatic force for different tip-sample distances (from 0 to 600 nm) and for different DC voltages applied to the tip (6 to 20 V) are shown and compared with experimental data in order to validate our approach. V C 2014 AIP Publishing LLC. [http://dx.

Charge packets in insulating polymers have been reported by many groups within the last two decades, especially in polyethylene-based materials. They consist in a pulse of net charge that remains in the form of a pulse as it crosses the insulation. In spite of a variety of characteristics depending on material properties and experimental conditions, one of the puzzling aspects of the packets is their repetitive character until they eventually die away. Several theories have been proposed to explain their formation and propagation. Two of them have the advantage of simplicity and of being physically based, being the existence of an hysteresis loop in the injection mechanism or a negative differential mobility of carriers with the electric field. Based on these descriptions, some progress has been done recently by discussing the shape of the packets during their propagation but none of the concepts has been incorporated into a transport model to describe the full evolution from the packet generation to their vanishing. Here, we used a simplified transport model featuring bipolar charge injection and transport coupled to specific conditions in charge injection or carrier mobility to reproduce experimental results. One of the salient features of the results is that both models are able to reproduce the repetitive character and the dying away of the packets that appear to be linked with the internal field distribution modulated by a bipolar space charge.

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