A finite weakest-link model of lifetime distribution of high-k gate dielectrics under unipolar AC voltage stress

This paper presents a new probability distribution function for the breakdown lifetime of high-k gate dielectrics under unipolar AC voltage stress. This function is derived from a finite weakest-link model, where the gate oxide layer is considered to consist of many potential breakdown cells. Each potential breakdown cell is modeled as a series coupling of several subcells, which is analogous to the fiber-bundle model for the strength statistics of structures. The present model indicates that the type of lifetime distribution varies with the gate area and the dependence of the mean lifetime on the gate area deviates from the classical Weibull scaling law. It is shown that the model agrees well with the observed lifetime histograms of HfO₂ based gate dielectrics under unipolar AC voltage stress.