Quantitative model for post-program instabilities in filamentary RRAM

This paper discusses and models the program instability observed in filamentary Hf-based RRAM devices in the context of the Hourglass model. It is demonstrated that two variability sources can be distinguished: (i) number variations of the amount of vacancies in the filament constriction and (ii) constriction shape variations. The shape variations are not stable in time and show a log(time)-dependent relaxation behavior after each programming pulse. This makes program/verify schemes, aiming at widening the resistive window, highly ineffective. We develop a quantitative, mathematical description of the instability using an auto-correlated step process of the shape parameters of the QPC conduction model.