Current-Gated Nonlinear Dynamics of a Self-Heating Memristor: an Electrothermal Extension of the Pickett Filamentary Model

Abstract

Self-heating couples the electrical and thermal states of filamentary memristors. However, the widely used Pickett compact model of $Ti{O}_2$ resistive switching is isothermal and therefore cannot capture the resulting electrothermal dynamics. We introduce the Arrhenius-Thermal Filamentary Model (ATFM), which extends Pickett's tunneling-gap kinetics by incorporating a dynamic heat balance and an Arrhenius-activated switching rate. The resulting electrothermal feedback produces a sharp current-gated transition: below a critical drive current, the tunneling gap undergoes a non-returning ratchet drift, whereas above it, exponential locking of the filament kinetics establishes a bounded, drive-locked electrothermal oscillation. Using a stroboscopic Poincaré map and the Floquet multipliers of the resulting period-$1$ orbit, we characterize this onset as a threshold-like orbit contraction rather than a classical local bifurcation. In the limit $E_a\to 0$, ATFM recovers the isothermal Pickett dynamics to numerical precision, as verified against an independent reference implementation over amplitude, frequency, and activation-energy sweeps. A variance-based Sobol' analysis with bootstrap confidence intervals identifies the excitation amplitude as the dominant control parameter and the thermal resistance $R_{th}$, rather than the thermal capacitance $C_{th}$, as the leading thermal contributor. A geometry-dependent temperature constraint further reveals a non-monotonic operating window in which an intermediate active area maximizes the switching excursion. The predicted trajectories are reproduced by both a fully behavioral SPICE netlist and a Verilog-A/OSDI device implementation, making ATFM directly suitable for circuit simulation. Overall, ATFM reveals and realizes a self-heating-driven dynamical regime within the widely used Pickett filamentary framework.

20 pages, 25 figures