JART v-ECM v1

A comprehensive, novel and consistent volatile ECM model is proposed that is derived from the nonvolatile physics-based model "JART ECM v1" comprising electrocrystallization, electron-transfer reactions at the interfaces and ionic migration as speed limiting ionic processes. Additionally, the electromotive force (emf) as counteracting force is introduced into the equation system enabling the simulation of volatile switching effects. Still, the model is consistent with previous results on the SET kinetics. The novelty of it stems from the theory of the nanobattery effect triggered by the emf. Earlier cyclic voltammetry measurements strongly hint towards a naturally intrinsic occurence of the emf within ECM-based systems which might be responsible for volatile properties of these systems. This model’s theory is supported by a clear insight that ionic processes triggering switching within such devices may occur as shifted in terms of the applied electric bias leading to non-zero crossing I-V characteristics. Including the emf to the model opens up a solid and good base for reproducing the volatile device’s dynamic behavior, such as correctly predicting the switching time or relaxation time upon programming with different bias strengths, and allows the model to become robust and consistent regarding nearly any experimental study. The model is implemented using Verilog-A, ready to be used with circuit simulators. [1] (a) 30 cycles of measured I-V sweeps of a Ag-HfO2-Pt ECM device stack are shown. A c2c variability is visible. (b) 30 cycles of simulated I-V sweeps are shown through the usage of the (variability-aware) volatile ECM model. [2] The experimentally measured threshold switching kinetics data points of a Ag-HfO2-Pt ECM device stack together with their d2d variability are displayed in red, whereas the simulated ones with their d2d variability are displayed in blue. [3] (a) The applied voltage signal to a Ag-HfO2-Pt ECM device stack in the measurement and in the simulation in order to investigate the device’s relaxation behavior. (b) The electric current flows through both devices. Here, a transient zoom of the electric current behavior in the measurement as well as in the simulation is shown around 1.04 ms. Once the current becomes smaller than 70 nA the relaxation time is measured: It is the time duration from the onset of the read voltage to the current crossing 70 nA. (c) Rseries = 560 kΩ, (d) Rseries = 1 MΩ: Measured and simulated relaxation time vs. applied voltage including d2d variability for two different series resistances.

本文提出了一种全面、新颖且一致的挥发性电化学金属化（Electrochemical Metallization, ECM）模型，该模型源自基于物理原理的非挥发性模型“JART ECM v1”，后者包含电结晶、界面处的电子转移反应以及作为限速离子过程的离子迁移。此外，本文将电动势（electromotive force, emf）作为反向力引入方程组，从而实现挥发性开关效应的仿真。该模型仍与此前关于置位（SET）动力学的研究结果保持一致。

本模型的创新之处在于由电动势触发的纳米电池效应理论。早期的循环伏安法测量结果强烈表明，基于ECM的器件体系中天然存在本征电动势，这或许正是此类体系具有挥发性特性的原因。

该模型的理论得到了一项明确认知的支撑：此类器件中触发开关行为的离子过程，会因外加电偏置发生偏移，从而呈现出非零截距的电流-电压（current-voltage, I-V）特性。在模型中引入电动势后，为复现挥发性器件的动态行为奠定了坚实基础——例如可准确预测不同偏置强度下编程时的开关时间或弛豫时间，同时使该模型在几乎所有实验研究场景下都具备鲁棒性与一致性。

本模型采用Verilog-A语言实现，可直接与电路仿真器配套使用。

[1] (a) 展示了Ag-HfO₂-Pt型ECM器件叠层的30次实测电流-电压（I-V）扫描循环，可见循环到循环（cycle-to-cycle, c2c）变异性。(b) 通过使用（考虑变异性的）挥发性ECM模型，得到了30次仿真电流-电压扫描循环结果。
[2] 以红色标注了Ag-HfO₂-Pt型ECM器件叠层的实验实测阈值开关动力学数据点及其器件间（device-to-device, d2d）变异性，蓝色标注则为对应的仿真结果及其器件间变异性。
[3] (a) 为探究器件弛豫行为，分别在实验测量与仿真中向Ag-HfO₂-Pt型ECM器件叠层施加的电压信号。(b) 展示了两款器件的电流响应，并在约1.04 ms处对实测与仿真的电流行为进行了瞬态放大。当电流小于70 nA时开始测量弛豫时间：其定义为从读取电压施加时刻到电流降至70 nA的持续时长。(c) 串联电阻Rseries=560 kΩ时的情况，(d) 串联电阻Rseries=1 MΩ时的情况：分别展示了两种串联电阻下，实测与仿真得到的弛豫时间随外加电压的变化关系，且包含了器件间变异性。