A phenomenological theory of correlated multiple soft-breakdown events in ultra-thin gate dielectrics

A general theory of the statistics of multiple breakdown events in ultra-thin gate oxides is developed. The standard theory of multiple breakdown events, based on Poisson statistics, allows only qualitative determination of the influence of each breakdown event on the rate of subsequent trap generation. In this paper, we develop a more general theory of multiple breakdown events to quantitatively determine the degree of correlation. This work allows one to calculate, regardless of the degree of correlation among the successive breakdown events, the statistical failure distribution of ICs as well as the time-dependent increase in the total leakage current during their operation. The theoretical description of leakage current not only explains a the experimental data reported in the literature to date, but also suggests a simple, yet fast experimental technique to determine the Weibull slope, the voltage- and the temperature-acceleration factors.