A maximum extreme-value distribution model for switching conductance of oxide-RRAM in memory applications

Abstract

In this work, we report an extensive experimental investigation of the important statistical properties of resistive random access memory (RRAM) switching conductance. We demonstrate the Gumbel statistics, a maximum extreme-value distribution for switching-filament conductance, as opposed to the minimum extreme-value distribution such as Weibull model. We apply a Poisson random statistical distribution for the spatial generation of percolation filaments to link the RRAM conductance measurements with device areas. As a result, we can derive two important relations: area scaling properties of percentiles and scale-factors. We show the validity of this maximum extreme-value distribution model by rigorously examining the vertical percentile-scaling characteristics of experimental data. The independently extracted shape-factor from the area-dependence of scale-factors captures the merged conductance distributions in good agreement with the experimental conductance data. It is revealed that larger variability associated with RRAM conductance measurements is directly linked to the maximum-valued statistical characteristics of this model. We also demonstrate that RRAM conductance, rather than resistance, is a fundamental statistical variable.