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 $(Q_{BD})$ 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.