Application of the defect clustering model for forming, SET and RESET statistics in RRAM devices

The choice of the right statistical model to describe the distribution of switching parameters (forming, SET and RESET voltages) is a critical requirement for RRAM, as it is used to analyze the worst case scenarios of operation that have to be accounted for while designing the cross-bar array structures, so as to ensure a robust design of the circuit and reliable data storage unit. Several models have been proposed in the recent past to characterize the voltage variations in VFORM, VSET and VRESET using the percolation framework. However, most of these models assume defect generation to be a Poisson process and apply the standard Weibull distribution for parameter extraction and lifetime extrapolation. Recent dielectric breakdown studies both at the front-end as well as back-end have shown that the Weibull statistics does not describe the stochastic trends well enough, more so in downscaled structures at the low and high percentile regions given the possibility of defect clustering which is either physics-driven or process quality-driven. This phenomenon of defect clustering is all the more applicable in the context of resistive random access memory (RRAM) devices, as switching occurs repeatedly at ruptured filament locations where defect clusters pre-exist. This study examines the validity of the clustering model for RRAM switching parameter statistics (time/voltage to FORM, SET and RESET) and presents a physical picture to explain the origin of clustering in RRAM. A large set of data from various published studies has been used here to test the suitability and need for a clustering model based reliability assessment. Dependence of the clustering factor on temperature, voltage, device area, dielectric microstructure and resistance state has also been examined.