A percolation based dielectric breakdown model with randomic changes in the dielectric constant

We describe a percolation based model for the dielectric breakdown of metal-oxide-semiconductor capacitors where the dielectric constant varies randomly throughout the oxide layer. We consider the SiO2 oxide within a rectangular lattice framework, and the breakdown is simulated as a cluster growth depending process where the local electric field is a function of the randomly varying permissivity. The effects of the bias polarity, oxide film thickness and electric field strength are discussed. We obtain that the slope of the Weibull distribution increases with the oxide thickness, which agrees with experimental results. Additionally, the oxide reliability as function of the electric field intensity can only be simulated using a percolative model if the electric field is considered to be local, i.e., the oxide is a conductor locally.