High-K dielectric stack percolation breakdown statistics

A cell-based analytical percolation model recently proposed for the dielectric breakdown (BD) of high-K stack gate dielectrics is reformulated in terms of competing local percolation paths. The model is equivalent to kinetic Monte Carlo implementation of percolation and it is shown to be consistent with large sample size statistical data. This is a physics-based picture that predicts the scaling of the BD distribution with the oxide area and with the thickness of each stack dielectric layer. As an application exercise, we consider the scaling of the stack reliability when the SiO₂-based interface layer thickness is scaled towards zero at constant equivalent oxide thickness (EOT).