Accurate model for time-dependent dielectric breakdown of high-k metal gate stacks

Time-dependent dielectric breakdown (TDDB) in high-k (HK) dielectric stacks is characterized by short breakdown times and shallow Weibull slopes. In this work, these observations are explained by a percolation model with different defect generation rates in the HK layer and interfacial SiO_x layer that form the stack. The difference in defect generation rate impacts the statistics of breakdown of the stack and bimodal distributions are obtained with a transition from a shallow to steep Weibull slope for large areas. It is shown that for a HK layer with a low initial defect density, long breakdown times and steep Weibull slopes are obtained for typical product areas, mitigating TDDB as a reliability show-stopper for HK dielectrics.