Dielectric breakdown in HfO₂dielectrics: Using multiscale modeling to identify the critical physical processes involved in oxide degradation

We use a multi-scale modeling to study the time-dependent dielectric breakdown of an amorphous (a-) HfO 2 insulator in a metal-oxide-metal capacitor. We focus on the role played by electron injection in the creation of oxygen vacancies, which eventually form the percolation path responsible for dielectric breakdown. In this scenario, the electron transport through the dielectric occurs by multi-phonon trap assisted tunnelling (MPTAT) between O vacancies. Energy parameters characterizing the creation of oxygen vacancies and the MPTAT process are calculated using density functional theory employing a hybrid density functional. The results demonstrate that the formation of neutral O vacancies facilitated by electron injection into the oxide represents a crucial step in the degradation process dominating the kinetics at common breakdown fields. We further show the importance of the so-called "energetic correlation"effect, where pre-existing O vacancies locally increase the generation rate of additional vacancies accelerating the oxide degradation process. This model gives realistic breakdown times and Weibull slopes and provides a detailed insight into the mechanism of dielectric breakdown and atomistic and electronic structures of percolation paths in a-HfO 2. It offers a new understanding of degradation mechanisms in oxides used in the current MOSFET technology and can be useful for developing future resistive switching and neuromorphic nanodevices.