## 2 Memristor: Models, Material, and Structure Design
### Memristor Modeling
The state equation of the TEAM model is represented by Equation (5) [21]:  
\[\frac{dx}{dt}=\left\{ \begin{array}{l}K_{off}\Big{(}\frac{i(t)}{t_{off}}-1 \Big{)}^{a_{off}}\quad f_{off}(x)\,\qquad 0<i_{off}<i\\ K_{on}\Big{(}\frac{i(t)}{t_{on}}-1\Big{)}^{a_{on}}\quad f_{on}(x)\,\qquad i<i_{on}<0\\ 0\,\quad\text{otherwise}\end{array} \right\} \tag{5}\]  
where \(i_{on}\) and \(i_{off}\) are current thresholds of the memristor, \(K_{off}\), \(K_{on}\), \(a_{off}\) and \(\alpha\)on are the fitting parameters, and \(f_{off}(x)\) and \(f_{on}(x)\) are the corresponding window functions of the memristor. The experimental results from numerous memristive devices show voltage thresholds rather than current thresholds. These voltage thresholds indicate that changes primarily influence the switching behavior of memristive devices in the voltage applied across them. This finding suggests that controlling the voltage levels can effectively modulate the state of these devices. In [22], the TEAM model is extended to include the Voltage ThrEshold Adaptive Memristor (VTEAM) model. The VTEAM model allows for a more accurate representation of the behavior of memristor devices, as it incorporates voltage threshold adaptation. This extension provides a better understanding of how voltage changes can affect these devices' state and functionality. Also, the VTEAM model is designed to mimic the behavior of biological synapses and enable synaptic plasticity in neuromorphic systems, allowing for dynamic adjustments of the voltage threshold, which enhances the device's ability to learn and adapt to different input patterns. The VTEAM model is defined by Equation (6) [22]. The voltage dependency is identical to that in Equation (5), except that the voltage thresholds impact it. \[\frac{dx}{dt}=\left\{ \begin{array}{l}K_{off}\Big{(}\frac{v(t)}{v}-1\Big{)}^ {a_{off}}\quad f_{off}(x),\qquad 0<v_{off}<v\\ K_{on}\Big{(}\frac{v(t)}{v_{on}}-1\Big{)}^{a_{on}}\quad f_{on}(x),\qquad v<v_{ on}<0\\ 0,\quad\text{otherwise}\end{array} \right\} \tag{6}\]  
The VTEAM model is considered generic since it can be applied to any memristor model, regardless of its specific characteristics or behavior. This flexibility allows researchers and engineers to utilize the VTEAM model as a versatile tool for analyzing and simulating various memristor devices in different applications. Additionally, the VTEAM model's adaptability enables it to accurately capture the dynamic behavior and non-linear properties of memristors, making it an invaluable resource in the field of memristor re search. This flexibility allows for a comprehensive study of memristor devices and their performance across various operating conditions, making the VTEAM model valuable in memristor research. Additionally, memristor modeling includes SPICE models, Verilog-A models, and behavioral models. These models allow researchers to simulate the behavior of memristors in different circuits and applications, providing valuable insights for design and optimization. Additionally, machine learning algorithms are being employed to further improve the accuracy and efficiency of memristor modeling. By incorporating machine learning techniques, researchers can enhance the predictive capabilities of these models and tailor them to specific applications. This intersection of memristor modeling and machine learning is paving the way for more sophisticated and reliable electronic devices in the future.