00_FEA1 - 556 IEEE Transactions on Dielectrics and...

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556 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 7 No. 4, August 2000 A Finite Element Method for the Determination of Space Charge Distributions in Complex Geometry 0. Paris and J. Lewiner Laboratoire d’Electricit6 GCnCrale Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris, Paris, France T. Ditchi, S. Hole and C. Alquie Laboratoire des Instruments et Systemes Universite Pierre et Marie Curie Paris, France ABSTRACT Electrical breakdown in insulators very often initiate near high field regions of the structure, as found near small-radius impurities or at electrode defects. This is attributed to the devel- opment of localized space charges. For this reason many efforts have been made to determine such charge. Various techniques are now available, but they are not directly applicable to com- plex geometries where it is difficult determine analytically the field configuration and thus the relation between the measured variables and the space charge distribution. To solve this problem, we propose to use a numerical simulation using a finite element method (FEM). In this paper we describe how it can be implemented in the case of the pressure wave propagation (PWP) method. It is shown that measured signals in insulating samples with divergent electric field regions are well fitted by simulations. We show that this allows for the determination of space charge distribution in such samples. 1 INTRODUCTION T is now well known that the buildup of space charge in diverging I field regions of insulating materials can lead to electrical tree growth and thus to breakdown phenomena. The presence of impurities or de- fects, in a material subjected to a high applied voltage, can be the cause for such high field concentrations. Various methods are being used cur- rently to observe charge injection in diverging field geometries, such as point/plane structures. These methods typically involve differential current measurements [l] or electroluminescence [2]. They all suggest, or confirm, that charge transfer occurs at metal-insulator interfaces. In both cases however, the charge transfer is deduced from the experi- ments through very indirect procedures. For this reason, it has been proposed to use presently available non- destructive methods for direct charge distribution measurements and particularly the pressure wave propagation (PWP) method [3-61. Sev- eral studies already have been carried out in such a geometry [7,8]. However, the relationship between the measured signal and the space charge density is quite complex. In order to interpret the observed data, we have developed a numer- ical simulation using a finite element method (FEM) [9]. It gives, for any space charge distribution, the current induced in the external circuit by the propagation of the pressure wave. By comparing the experimental and simulated currents it is possible to determine, by successive ad- justments of the parameters used in the simulation, the unknown space charge distribution.
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This note was uploaded on 06/08/2011 for the course ELECTRICAL 124 taught by Professor Ghjk during the Spring '11 term at Institute of Technology.

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00_FEA1 - 556 IEEE Transactions on Dielectrics and...

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