Theoretical justification for the log-normal distribution of time dependent breakdowns in MOS oxides

This work presents the development of a physical model which predicts the log-normal time dependence observed for MOS oxide breakdown events during constant voltage stressing. It is assumed that the instantaneous probability for breakdown is directly proportional to the oxide current density which arises from a Fowler-Nordhiem tunneling mechanism. The electric field which produces the tunneling is enhanced by oxide defects and retarded by electron trapping in the oxide. The incorporation of a field enhancement distribution function approximates the reality of nonuniform defect sizes throughout the sample population, and provides a tool for quantifying oxide quality.