Microscopic Modeling of Electrical Stress-Induced Breakdown in Poly-Crystalline Hafnium Oxide Dielectrics

We present a quantitative physical model describing degradation of poly-crystalline ${\rm HfO}_{2}$ dielectrics subjected to electrical stress culminating in the dielectric breakdown (BD). The model accounts for the morphology of the hafnium oxide film and considers the interaction of the injected electrons with the atomic defects supporting the charge transport to calculate the 3-D power dissipation and temperature maps across the dielectric. This temperature map, along with that of the electric field, is used to self-consistently calculate the stress-induced defect generation rates in the dielectric during stress. The model quantitatively reproduces the evolution of the currents measured on ${\rm HfO}_{2}$ MIM capacitors during constant voltage stress, up to the onset of BD, and the dependencies of the time-dependent dielectric breakdown distributions on stress temperature and voltage. It represents a powerful tool for statistical reliability predictions that can be extended to other high- $\kappa$ materials, multilayer stacks, and resistive RAM devices based on transition metal oxides.