A new model for the breakdown dynamics of ultra-thin gate oxides based on the stochastic logistic differential equation

Progressive breakdown of ultra-thin (t_ox≈2 nm) oxides in MOS capacitors is simulated by means of a stochastic logistic process. The model is formulated as an Ito-type differential equation for the conductance and consists of a deterministic term that describes what occurs on average to the system and a random term that deals with the noisy behavior. Instead of considering a detailed description of every physical aspect involved, the proposed model is fundamentally aimed at capturing the degradation dynamics using a small set of parameters. However, despite its seemingly simple formulation, a close look at the numerical simulation scheme is imperative needed in order to understand the Output results as well as its potential pitfalls.