Electrothermal Compact Drift Model of TiO2 Memristors: Verilog-A Implementation and Dimensionless Regime Mapping
Abstract
Compact models of titanium-dioxide memristors used in circuit simulation commonly follow the drift formulation of Strukov \textit{et al.} and assume a constant ionic mobility, although oxygen-vacancy migration is thermally activated and Joule self-heating is unavoidable. We present ATDM (Arrhenius Thermally Activated Drift Model), a minimal electrothermal compact model that couples the drift equation to a lumped heat balance through an Arrhenius mobility. It adds one thermal state while preserving the electrical state variable, the relation v=iR(x), and the isothermal limit. The model is implemented in \textsc{Verilog-A}, compiled with OpenVAF, and simulated as a device in \texttt{ngspice}, where it reproduces an independent reference implementation within 0.009 % of the peak voltage and recovers the isothermal excursion at zero activation energy. A dimensionless formulation introduces a thermal lag ε and an effective switching number Θ. Across 2.5×105 simulations, Θ orders the state-variable excursion over the tested quasi-static domain with a robust relative scatter of 4 % and no fitted constant, and the (ε,Θ) regime map quantifies when the quasi-static thermal reduction remains valid. Under current drive, the stroboscopic map of the reduced model is proved to be strictly increasing, which excludes period-doubling and chaos in that reduction. Within the sampled ranges, a variance-based sensitivity analysis identifies the effective thermal resistance as a first-order contributor to self-heating, while separate capacitance sweeps show a weak influence of the thermal capacitance in the quasi-static regime. The results characterize the specified model with representative, uncalibrated parameters.
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BibTeX
@misc{koudafoke2026electrothermal,
title = {{Electrothermal Compact Drift Model of TiO$_2$ Memristors: Verilog-A Implementation and Dimensionless Regime Mapping}},
author = {N. G. Koudafokê and Hilda A. Cerdeira and L. A. Hinvi and A. V. Monwanou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26815},
eprint = {2609.26815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26815},
}
RIS
TY - UNPB
TI - Electrothermal Compact Drift Model of TiO_2 Memristors: Verilog-A Implementation and Dimensionless Regime Mapping
AU - N. G. Koudafokê
AU - Hilda A. Cerdeira
AU - L. A. Hinvi
AU - A. V. Monwanou
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.26815
UR - https://arxiv.org/abs/2609.26815
AB - Compact models of titanium-dioxide memristors used in circuit simulation commonly follow the drift formulation of Strukov \textit{et al.} and assume a constant ionic mobility, although oxygen-vacancy migration is thermally activated and Joule self-heating is unavoidable. We present ATDM (Arrhenius Thermally Activated Drift Model), a minimal electrothermal compact model that couples the drift equation to a lumped heat balance through an Arrhenius mobility. It adds one thermal state while preserving the electrical state variable, the relation v=iR(x), and the isothermal limit. The model is implemented in \textsc{Verilog-A}, compiled with OpenVAF, and simulated as a device in \texttt{ngspice}, where it reproduces an independent reference implementation within 0.009 % of the peak voltage and recovers the isothermal excursion at zero activation energy. A dimensionless formulation introduces a thermal lag ε and an effective switching number Θ. Across 2.5×10^5 simulations, Θ orders the state-variable excursion over the tested quasi-static domain with a robust relative scatter of 4 % and no fitted constant, and the (ε,Θ) regime map quantifies when the quasi-static thermal reduction remains valid. Under current drive, the stroboscopic map of the reduced model is proved to be strictly increasing, which excludes period-doubling and chaos in that reduction. Within the sampled ranges, a variance-based sensitivity analysis identifies the effective thermal resistance as a first-order contributor to self-heating, while separate capacitance sweeps show a weak influence of the thermal capacitance in the quasi-static regime. The results characterize the specified model with representative, uncalibrated parameters.
ER -