An Improved Description of the Dielectric Breakdown in Oxides Based on a Generalized Weibull distribution

TL;DR

This paper introduces a generalized Weibull distribution model incorporating fluctuations to better describe dielectric breakdown in ultra-thin oxides, enhancing reliability predictions for electronic devices.

Contribution

It presents a physically motivated $q$-Weibull distribution model that accounts for oxide thickness fluctuations, improving breakdown data analysis and extrapolation methods.

Findings

$q$-Weibull distribution effectively fits experimental breakdown data.

Incorporating fluctuations improves reliability assessment.

Model connects with Tsallis statistics for physical interpretation.

Abstract

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.