Failure of Weibull distribution to represent switching statistics in OxRAM

Abstract

Considering the reasonable similarity in the physical mechanisms governing oxide breakdown and filamentary resistive switching, the use of the Weibull distribution has been widespread in the RRAM community for describing the stochastics of Forming, SET, RESET and read disturb data sets. Upon close examination, it is apparent that the Weibull fitting tends to be poor at the high percentiles for most of these data sets in RRAM (both vacancy based (OxRAM) and metal filament (CBRAM) based switching). The fundamental origin of these deviations is investigated in this work for OxRAM stacks through an analytical model making use of the percolation theory as the backbone framework and considering the physical process of thermochemical bond breaking that governs forming and SET events in resistance switching and the cycle-to-cycle variability inherent in the filament size and shape due to these atomistic events. Our model is compared with the standard Weibull distribution for fitting several data sets reported in the literature. The recently proposed defect clustering model is shown to be a better representative of the statistical physics governing the forming and SET switching process.