Recent advances in the polyfilamentary model for electronic conduction in electroformed insulating films

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Abstract
A state-of-art review is presented of modifications introduced to the original polyfilamentary model for electronic conduction in electroformed insulating films. The solution of the one-dimensional heat equation, satisfying some physically realistic boundary conditions, is believed to be the best technique for describing thermal dissipation. New criteria based upon thermal loss through the positively biased electrode are obtained for the occurrence of voltage-controlled negative resistance. Different types of distributions of filamentary parameters are considered, and the normal distributions of the values of radii and resistivities among the filament population are found to provide a satisfactory basis for determining current-voltage characteristics for metal/insulator/metal structures. The experimentally observed shift in the peak of the I(V) characteristics is explained in terms of variations in the statistical parameters characterizing a probability density function for the distributions.