Statistical outlook into the physics of failure for copper low-k intra-metal dielectric breakdown

The degradation of low-k dielectrics is analyzed from a trap-assisted tunneling (TAT) current perspective assuming a Poole-Frenkel (P-F) conduction mechanism. A robust probabilistic failure model is developed which accounts for the development of traps at the low-k-SiN capping layer interface which is believed to be the weak link for evolution of low-k dielectric failure mechanisms. The developed model also accounts for the bond breaking phenomenon as dangling bonds are suggested to be the functional form of trap centers during the evolution of the percolation path. The new model is observed to provide an accurate fit to the failure data in the literature. The statistical nature of time-dependent dielectric breakdown (TDDB) failure is shown to be dependent on the definition of failure and based on the conventional definition of catastrophic leakage current increase, we show that the Lognormal distribution is inapplicable and that the Weibull stochastics needs to be used. Statistical analysis of TDDB data clearly indicates the presence of bimodal failure distributions indicating the presence of two failure mechanisms. Further investigation is necessary to uncover the nature and physics governing these different failure mechanisms. A three-parameter Weibull model is suggested to be appropriate for modeling Cu-induced TDDB failures where an incubation time exists for Cu out-diffusion.