An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution

In this work, we address modal parameter fluctuations in statistical distributions describing charge-to-breakdown (QBD) and/or time-to-breakdown (tBD) during the dielectric breakdown regime of ultra-thin oxides, which are of high interest for the advancement of electronic technology. We reobtain a generalized Weibull distribution (q-Weibull), which properly describes (tBD) data when oxide thickness fluctuations are present, in order to improve reliability assessment of ultra-thin oxides by time-to-breakdown (tBD) extrapolation and area scaling. The incorporation of fluctuations allows a physical interpretation of the q-Weibull distribution in connection with the Tsallis statistics. In support to our results, we analyze tBD data of SiO2-based MOS devices obtained experimentally and theoretically through a percolation model, demonstrating an advantageous description of the dielectric breakdown by the q-Weibull distribution.