F. Baudoin

Charge dynamics and its energetic features in polymeric materials

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 polyethylene-based 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).

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 Poissons 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.

Charge transport modelling in electron-beam irradiated dielectrics: a model for polyethylene

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 constraints on fitting parameters that must comply to a set of experimental results.

Space charge modeling in electron-beam irradiated polyethylene: Fitting model and experiments

A numerical model for describing charge accumulation in electron-beam irradiated low density polyethylene has been put forward recently. It encompasses the generation of positive and negative charges due to impinging electrons and their transport in the insulation. However, the model was not optimized to fit all the data available regarding space charge dynamics obtained using up-to-date pulsed electro-acoustic techniques. In the present approach, model outputs are compared with experimental space charge distribution obtained during irradiation and post-irradiation, the irradiated samples being in short circuit conditions or with the irradiated surface at a floating potential. A unique set of parameters have been used for all the simulations, and it encompasses the transport parameters already optimized for charge transport in polyethylene under an external electric field. The model evolution in itself consists in describing the recombination between positive and negative charges according to the Langevin formula, which is physically more accurate than the previous description and has the advantage of reducing the number of adjustable parameters of the model. This also provides a better description of the experimental behavior underlining the importance of recombination processes in irradiated materials.

Modeling electroluminescence in insulating polymers under ac stress: effect of excitation waveform

A charge transport model allowing the description of electroluminescence in polyethylene films under ac stress is proposed. The fluid model incorporates bipolar 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 of the density of positive and negative carriers during sinusoidal, triangular and square 50Hz 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 10 nm away from the electrode where the mobility is increased as compared with the bulk mobility due to the high density of charge. The approach is very encouraging and opens the way to model space charge under time-varying voltages.

Study of signal treatment for a pulsed electro-acoustic measurement cell: a way of improving the transfer matrix condition number

This work is focused on the improvement of the condition number of the transfer function matrix in a pulsed electro-acoustic (PEA) cell. A numerical electro-acoustic model is developed with the software COMSOL. This model is one-dimensional and the system of equations with partial differential functions is solved using a finite element method in non-stationary situations. Using this model, we can establish the output voltage of the piezoelectric sensor and acoustic pressure at each point of the calculation domain. Our approach consists in recovering the charge distribution within the sample using a deconvolution method between the simulated output voltage and the transfer function of the PEA cell. Results show why some changes of the PEA cell such as the nature of materials or sensor geometry involve an ill-posed problem or ill-conditioned problem, and why other arrangements lead to a well-conditioned problem, more amenable to giving the appropriate solution.

Multi-dimensional modelling of electrostatic force distance curve over dielectric surface: Influence of tip geometry and correlation with experiment

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.

Charge packets modeling in polyethylene

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.

Contribution to improving the spatial resolution of a pulsed electro acoustic cell measurement: An analysis of acoustics waves propagation

This work aims at improving the spatial resolution for the pulsed electro-acoustic method — PEA. Whatever the measurement principle considered, the best spatial resolution achieved so far is of the order of several micrometers, being at most 10µm in case of the PEA method. This limit constitutes a drawback when considering rather thin insulating layers (order of tens of µms), as the case in some capacitors or in films layed on outer parts of satellites. Also, a better resolution is expected to provide a better description of charge generation in insulations at metal dielectric interfaces or under low energy electron beam. This work is focused on acoustic waves propagation inside the PEA cell and the analysis of influence of piezoelectric transducer geometrys of the quality of output voltage signal.

Input of optimization techniques for implementing charge transport models in electrical insulation

This work aims at systematizing the determination of physical parameters pertaining to charge transport models for dielectrics through the use of a method based on Levenberg-Marquardt algorithm. Experimental data used are net density of charge as measured by the pulsed electro-acoustic method — PEA — and external charging and discharging current measurements. Simulated data are those produced by a bipolar charge transport model developed for low density polyethylene under dc stress. We show that the optimization tool developed as an interface between the numerical model and the experimental data can readily produce a set of values of physical parameters for the model.