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 TiO2 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 Ea→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 Rth, rather than the thermal capacitance Cth, 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.
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BibTeX
@misc{koudafoke2026currentgated,
title = {{Current-Gated Nonlinear Dynamics of a Self-Heating Memristor: an Electrothermal Extension of the Pickett Filamentary Model}},
author = {N. G. Koudafokê and Florian Günther and Hilda A. Cerdeira and A. V. Monwanou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03057},
eprint = {2609.03057},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03057},
}
RIS
TY - UNPB
TI - Current-Gated Nonlinear Dynamics of a Self-Heating Memristor: an Electrothermal Extension of the Pickett Filamentary Model
AU - N. G. Koudafokê
AU - Florian Günther
AU - Hilda A. Cerdeira
AU - A. V. Monwanou
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03057
UR - https://arxiv.org/abs/2609.03057
AB - Self-heating couples the electrical and thermal states of filamentary memristors. However, the widely used Pickett compact model of TiO_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→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.
ER -