Toy model for the progressive breakdown dynamics of ultrathin gate dielectrics

A simple analytic model for the progressive breakdown (BD) dynamics of ultrathin) gate oxides is presented. It is shown how the interplay between series and parallel resistances that represent the breakdown path and its surroundings leads to a sigmoidal I-t characteristic compatible with experimental data. The analysis is carried out using the Lyapunov exponent and the potential function associated with the logistic equation for the leakage current. The roles played by the initial current value and the system's attractor in the breakdown trajectories are discussed.