M. Rouff and J.-M. Reboul (France)
ATWM, space charge measurement, nondestructive method, Ck spline functions, inverse problem, Ck continuous interpolation of distributed parameters
Space charge measurement is a recognized technique for the characterization of insulating materials. Nevertheless in the case of thin films, experimental difficulties arise and, at best, the space charge may be deduced by identification with equivalent discrete distributions. Because of the use of models based on multiple derivations of the experimental signal these identifications lead to an image of a discretized distribution of the space charge with a very large uncertainty. Our Laboratory has gained significant experimental advances [1], to achieve with a good precision the identification of the one dimensional continuous distribution of the space charge density. This work is concerned with dielectric thin films for power capacitors with possible extensions to dielectric layers used in MOSFET or IGBT. We present in this article a new analytic model for the identification of the continuous one dimensional density of space charge distribution for thin insulator samples (<100 µm) that does not require multiple derivations. In fact only one integration is needed, with an obvious robustness result of the identification method versus the experimental results. This integral equation requires the identification of a nonlinear kernel that is the density of the one dimensional space charge distribution. Thanks to the algebraic and differential properties of Ck spline functions [2,3] we can compute this nonlinear kernel with an arbitrary good precision [4].
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