TiO$_2$忆阻器的电热紧凑漂移模型：Verilog-A实现与无量纲区间映射
Electrothermal Compact Drift Model of TiO$_2$ Memristors: Verilog-A Implementation and Dimensionless Regime Mapping
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中文总结 AI 辅助
本文提出ATDM电热紧凑模型，耦合漂移方程与热平衡，通过无量纲映射和仿真验证，有效表征忆阻器自热效应。
中文摘要 AI 辅助
电路仿真中使用的二氧化钛忆阻器紧凑模型通常遵循Strukov等人的漂移公式，并假设离子迁移率为常数，尽管氧空位迁移是热激活的，且焦耳自热不可避免。我们提出了ATDM（Arrhenius热激活漂移模型），这是一种最小电热紧凑模型，通过Arrhenius迁移率将漂移方程与集总热平衡耦合。它增加了一个热状态，同时保留了电状态变量、关系$v=iR(x)$和等温极限。该模型在\textsc{Verilog-A}中实现，用OpenVAF编译，并在\texttt{ngspice}中作为器件进行仿真，在峰值电压的$0.009\\,\\%$范围内重现了独立的参考实现，并在零激活能下恢复了等温偏移。无量纲公式引入了热滞后$\varepsilon$和有效开关数$\Theta$。在$2.5\times10^{5}$次仿真中，$\Theta$在测试的准静态域内对状态变量偏移进行排序，具有稳健的$4\\,\\%$相对散布，且无需拟合常数，$(\varepsilon,\Theta)$区间图量化了准静态热还原何时仍然有效。在电流驱动下，证明了简化模型的频闪映射严格递增，这排除了该简化中的倍周期分岔和混沌。在采样范围内，基于方差的敏感性分析将有效热阻确定为自热的一阶贡献者，而单独的电容扫描显示热电容在准静态区间内影响较弱。结果用代表性的、未校准的参数表征了指定模型。
英文摘要
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 $\varepsilon$ and an effective switching number $Θ$. Across $2.5\times10^{5}$ 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 $(\varepsilon,Θ)$ 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.
发表机构
- ICTP South American Institute for Fundamental Research, Instituto de Física Teórica (IFT–UNESP)（国际理论物理中心南美基础研究所，圣保罗州立大学理论物理研究所）
- Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey Calavi (UAC)（数学与物理科学研究所，阿波美-卡拉里大学）
- Laboratoire des Procédés et de l’Innovation Technologiques (LaPIT), Institut National Supérieur de Technologie Industrielle (INSTI) Lokossa/UNSTIM（工艺与技术创新实验室，洛科索国家高等工业技术学院）
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