Equilibrium analysis of Mott memristor reveals criterion for negative differential resistance

Abstract

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