Degradation dynamics of ultrathin gate oxides subjected to electrical stress

The sigmoidal behavior exhibited by the current-time characteristics of constant voltage-stressed metal-oxide-semiconductor (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 mathematically describe this dynamical process we consider a classical model of population growth theories such as the Verhulst differential equation. The role that might play the background tunneling current in the evolutionary trajectory of the breakdown event is also discussed.