Statistical Modeling of Time-Dependent Post-Programming Conductance Drift in Analog RRAM

The post-programming conductance drift of analog resistive random-access memory (RRAM) is a critical reliability issue and could result in performance degradation in RRAM- based neuromorphic computing systems. It is necessary to model the conductance drift behavior in order to better evaluate the performance of analog RRAM and customize algorithms to accommodate it. This work investigated the statistical modeling for post-programming conductance drift of 3-bit analog RRAM. We proposed a novel criterion, weighted root mean square error (WRMSE), to substantiate that the conductance drift ought to be separated into two distinct phases: immediate post-programming conductance drift, i.e. relaxation, and more stable fluctuations that occur seconds after programming, i.e. random telegraph noise (RTN). We further developed a compact model based on continuous-time Markov chain (CTMC) to capture the variation of post-programming conductance distribution, which well fitted the skewed conductance distribution. The established model of post-programming conductance drift could provide useful guidelines for the future design of analog-RRAM based neuromorphic computing systems.