Equilibrium analysis of Mott memristor reveals criterion for negative differential resistance

Two-terminal electronic devices that exhibit voltage-controlled threshold switching (TS) via negative differential resistance (NDR) are important for many emerging applications. Pickett and Williams developed what has become a well-known physics-based model nanoscale exhibiting NDR due to reversible insulator-metal phase (Mott) transition. The Mott memristor couples changes in electrical Joule heating the of material using one dynamic state variable, u, describes volume fraction metal cross section device. formulation involves nonlinear first-order ordinary equation eight physical parameters. New equilibrium analysis reveals simple condition determines whether predicts required current–voltage (i–v) hysteresis operation. We show S-shaped (also called current-controlled NDR) arises only above critical ratio, Mc, insulator resistivity. Specifically, i–v plane cannot occur below Mc=e2+1?8.39 (i.e., e?2.718…; Euler's number), but this value appears. This understanding enables tuning hysteretic features, including voltages resistive switching, which benefit use TS memristors as memory storage elements, well excitable mimicking neural action potentials.