Comprehensive Methodology for Multiple Spots Competing Progressive Breakdown for BEOL/FEOL Applications
We present the general framework of dielectric breakdown (BD) showing multiple spot competing progressive breakdown (PBD) in BEOL/FEOL applications in the presence of thickness variability. A Monte-Carlo simulation procedure is used to investigate post-BD phenomena from small thickness variation in FEOL SiO2 to very large variations in BEOL low-K dielectrics. Rather than directly modelling current transients as done recently , we apply successive BD statistics methodology to generate multiple BD spots and their associated progressive breakdown time (TPBD). We show that for single-spot PBD mode the first BD time (TBD or TBD1) is intrinsically uncorrelated to its residual time (TRES) even if the variability is present. In contrast, in the case of multiple-spot competing PBD, the final hard breakdown (HBD) distributions are fundamentally affected by thickness variation so that they become non-Weibull and deviate from Poisson area scaling at high percentiles. We report an important intrinsic correlation between TBD and TRES results involving multiple spot PBD if thickness variability is present. Our MC simulation results are in excellent agreement with experimental data for three sets of hardware from FEOL and BEOL applications.