Logistic model for leakage current in electrical stressed ultra-thin oxides

It is shown that the leakage current flowing through an ultra-thin gate oxide in a metal-oxide-semiconductor structure subjected to a constant voltage stress can be described by a Verhulst-type logistic model. An exponential growth at the outset is followed by a saturation in the conduction characteristic, which indicates that, after a rapid expansion, the damaged area reaches an upper bound. This sigmoidal behaviour is interpreted as a self-constrained growth of the leakage site population.