Statistical insight into controlled forming and forming free stacks for HfOx RRAM

Abstract

Percolation model used to optimize oxide and cap thickness for forming-free RRAM.Hot helps reduce variability in the forming voltage statistics.Quantum point contact formulation has been used to explain hot forming.Forming is two-stage process involving filament nucleation (SBD) and growth (PBD).Convolution of filament nucleation and growth gives non-Weibullian statistics. We present a statistical perspective based on the percolation model and defect generation kinetics that explains the variability in forming conditions for ultra-thin HfOx-based RRAM devices as a function of the temperature, dielectric (tox) and metal cap (tCAP) thickness. Forming is to be perceived as a two-stage process consisting of oxygen vacancy filament nucleation (percolation) and subsequent filamentary growth (wear-out), corresponding to the soft (SBD) and progressive breakdown (PBD) regimes in oxide reliability. The convolution of these two processes explains the non-Weibullian trends in forming voltage and resistance statistics. The reduction in forming variability at high temperatures (hot forming) is explained using the insensitivity of vacancy generation to local electric field variations induced by the dynamic fluctuations in the post-SBD filament configuration using the quantum point contact (QPC) formulation. Using our design of experiments, an optimum tox:tCAP ratio for forming-free realization of RRAM is also determined.