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 SiOx 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.

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