When a metal-oxide-semiconductor structure with a hyper-thin (≤2nm) dielectric film is subjected to constant voltage stress, after the triggering of the breakdown event, the leakage current increases progressively over time until saturation. In this work, we propose a logistic-type growth model that allows capturing the non-symmetrical features of the trajectory exhibited by the current-time characteristics. It is discussed how the resulting solution could be used to evaluate the time-to-failure under different stress conditions.