  In this work, we address modal parameter fluctuations in statistical
distributions describing charge-to-breakdown $(Q_{BD})$ and/or
time-to-breakdown $(t_{BD})$ 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 $(t_{BD})$ data when oxide thickness fluctuations are
present, in order to improve reliability assessment of ultra-thin oxides by
time-to-breakdown $(t_{BD})$ 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 $t_{BD}$ data of SiO$_2$-based MOS devices obtained
experimentally and theoretically through a percolation model, demonstrating an
advantageous description of the dielectric breakdown by the $q$-Weibull
distribution.
