Modeling and tuning the filament properties in RRAM metal oxide stacks for optimized stable cycling

Forming current I_form is a crucial parameter for stable cycling in a HfO₂ RRAM stack. (i) Too low I_form results in constriction `elongation' for filament current reduction during reset, quickly leading to failure. (ii) Too high and unlimited I_form leads to poor control of the filament nature expressed as a wide V₀-distribution in the QPC model. (iii) In between, I_form is directly correlated to the minimal achievable HRS current and a narrow, stable filament is formed which allows for device scaling as well as multi-level programming.