SPICE simulation of the time-dependent clustering model for dielectric breakdown

In this letter, a method for dealing with the time-dependent dielectric breakdown (TDDB) of oxide layers in MOS and MIM structures in the framework of SPICE simulations is reported. In particular, we focus the attention on the clustering model (Burr's XII distribution) for dielectric breakdown which can be considered an extension of the well known Weibull model. The oxide time-to-breakdown for both models is calculated using the inversion method for the cumulative distribution function. For the sake of completeness, the proposed approach includes uncorrelated variability both in the initial and final resistance states. For illustrative purposes, it is also shown how voltage acceleration, progressive breakdown or any other correlation factor can be introduced in the simulation parameters. As an application example, the proposed method is used to simulate the simplest case of a gate-to-drain dielectric breakdown of a NMOS-based inverter circuit.