Logistic modeling of progressive breakdown in ultrathin gate oxides

The sigmoidal behavior exhibited by the current-time characteristics of constant voltage stressed MOS capacitors with ultrathin oxides is ascribed to a self-constrained increase of the leakage sites population that assist the conduction process between the electrodes. To analytically describe this dynamical process we consider a classical model of population growth theories such as the Verhulst differential equation. The role played by the background tunneling current in the detection of the breakdown event is also discussed.