A physics-based model of the dielectric breakdown in HfO2 for statistical reliability prediction

We present a quantitative physical model describing the current evolution due to the formation of a conductive filament responsible for the HfO₂ dielectric breakdown. By linking the microscopic properties of the stress-generated electrical defects to the local power dissipation and to the corresponding temperature increase along the conductive path the model reproduces the rapid current increase observed during the breakdown. The model successfully simulates the experimental time-dependent dielectric breakdown distributions measured in HfO₂ MIM capacitors under constant voltage stress, thus providing a statistical reliability prediction capability, which can be extended to other high-k materials, multilayer stacks, resistive memories based on transition metal oxides, etc.