Memristor Modeling -- Static, Statistical, and Stochastic Methodologies

Memristor, the fourth passive circuit element, hasattracted increased attention since it was rediscovered by HPLab in 2008. Its distinctive characteristic to record the historicprofile of the voltage/current creates a great potential for futureneuromorphic computing system design. However, at the nanoscale, process variation control in the manufacturing of memristordevices is very difficult. The impact of process variations on amemristive system that relies on the continuous (analog) statesof the memristors could be significant. In addition, the stochasticswitching behaviors have been widely observed. To facilitate theinvestigation on memristor-based hardware implementation, wecompare and summarize different memristor modeling methodologies, from the simple static model, to statistical analysis bytaking the impact of process variations into consideration, andthe stochastic behavior model based on the real experimentalmeasurements. In this work, we use the most popular TiO₂ thin film device as an example to analyze the memristor´selectrical properties. Our proposed modeling methodologies canbe easily extended to the other structures/materials with necessarymodifications.