Stochastic variability of vacancy filament configuration in ultra-thin dielectric RRAM and its impact on OFF-state reliability

Considering SET and RESET to be dynamic stochastic processes involving the generation-recombination and drift-diffusion of multiple oxygen ions / vacancies, we examine the microscopic statistical changes in the shape of the filament during multiple switching cycles in ultra-thin low-power HfO_x-based RRAM. The effect of forming compliance, dielectric microstructure, multi-layer dielectric films and Al-doping on the variability in the filament geometry is investigated based on the quantum point contact (QPC) formulation [1, 2]. The stability (reliability) of the filament in the OFF-state to non-equilibrium vacancy-induced perturbations is evaluated using the disturb voltage (V_DIST). Microscopic changes of the defect arrangement in the OFF-state have a big influence on the filament stability. The final configuration of the filament in the OFF-state is bimodal with a finite non-zero probability of being in the QPC mode or entering the tunnel barrier (TUN) mode.