From Accelerated to Operating Conditions: How Trapped Charge Impacts on TDDB in SiO₂ and HfO₂ Stacks

Despite the various well-established theories such as the thermochemical (E-model), $\surd $ E-model, power law $(V^{N}$ -model), and 1/E-model, accurately replicate dielectric breakdown (BD) experimental trends in accelerated conditions, they diverge significantly in lifetime estimations when projecting to operating conditions. The recently introduced Carrier Injection (CI) model successfully reconciles the discrepancies observed in the aforementioned theories within a unified framework, revealing that the time-dependent dielectric breakdown (TDDB) E-field dependence can change from thermochemical to power-law, and even to 1/E trend, depending on the microscopic properties of key atomic species (precursors). Notably, these findings were based on the assumption that the electric field in the dielectric is solely influenced by the applied bias, disregarding the impact of trapped charge at defects and precursors. Nevertheless, it is recognized that trapped charge significantly contributes to the local electric field within the oxide at low applied voltages, leading to a substantial difference between accelerated and operating conditions. With that in mind, this paper incorporates the influence of trapped charges into the CI model, offering a more complete explanation of the BD phenomenon in SiO2 and HfO2 stacks. The research demonstrates that, depending on the material system and the nature of defect precursors in the oxide, the presence of trapped charge can result in significant deviations from TDDB lifetime predictions derived from conventional models. Furthermore, the study explores the combined impact of trapped charge and the microscopic properties of defect precursor sites on TDDB and leakage current through the oxide.