Applications of clustering model to bimodal distributions for dielectric breakdown

In this work, the authors report the extensive time-to-breakdown (TBD) data collected from back end of line/middle of the line and metal insulator metal capacitor dielectrics that exhibit not only non-Poisson area scaling but also multiple modal (or bimodal) breakdown characteristics. They develop a new bimodal modeling approach of the distributed competition process in conjunction with the time-dependent clustering model to extract the breakdown parameters and the characteristic breakdown time and slope (t63 and β) from this seemingly intractable breakdown data. While the number of parameters increases as a result of an increase in data complexity, these extracted parameters are consistent with Poisson area-scaling of fundamental weakest-link characteristics, and can thus be used for reliability projection. As a result, our modeling approach involving clustering model provides an important solution for technology qualification and dielectric-integrity assessment.