Elapsed-time statistics of successive breakdown in the presence of variability for dielectric breakdown in BEOL/MOL/FEOL applications

Abstract

We present the general framework of elapsed-time statistics of successive breakdown (BD) events in application to multiple-spot BD in the presence of variability. We show that the elapsed-times between successive BD events due to multiple BD spots (or filaments) are statistically distributed and contribute significantly to total post-BD margins in the case of multiple-spot progressive BD. Unlike the first BD events following Weibull statistics without variability, we demonstrate that elapsed-time distributions are fundamentally non-Weibull with much broader distributions as compared to the first BD statistics. The elapsed-times between successive BD events can be longer or shorter than the first BD time, depending on the Weibull slopes of the first BD distribution. Our simulation results of elapsed-time statistics are shown in good agreement with experimental data of FEOL and BEOL dielectrics with and without variability. This methodology paves the way for the correct implementation of multiple-spot progressive BD methodology for BEOL dielectrics in the presence of variability.