Resistive random access memory device (RRAM) has been widely used in various novel circuit systems, such as memory, artificial intelligence, and neural networks, due to its unique memory characteristics. However, there are very few studies focusing on analytic modeling of RRAM. In this article, modeling for solving analytic approximate solution to the state variable of RRAM, based on the proposed Multistage Homotopy Analysis Method (MuHAM), is proposed. Different from traditional HAM, the time span under consideration is divided into many subintervals, then the convergence control parameter in each subinterval is optimized to achieve high approximation accuracy. By simulating and comparing the obtained analytic solutions with solutions solved by other traditional homotopy-based modeling methodologies and by numerical analyses, we verified that MuHAM has higher Quality Factor (introduced to evaluate the model accuracy and computational cost comprehensively), hence improving the simulation efficiency. Besides the classical Hewlett-Packard (HP) RRAM, some current RRAMs are also verified. MuHAM also has the advantages of enabling both qualitative and quantitative analyses, and immunity to convergence issues. It is particularly suitable for the analytic modeling of the other novel memory devices having strong nonlinearity.

中文翻译：

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基于多级同伦分析法的RRAM解析建模

电阻式随机存取存储器（RRAM）由于其独特的存储特性，被广泛应用于各种新型电路系统，如存储器、人工智能和神经网络。然而，很少有研究关注 RRAM 的分析建模。在本文中，基于所提出的多级同伦分析方法 (MuHAM)，提出了求解 RRAM 状态变量解析近似解的建模方法。与传统HAM不同的是，将考虑的时间跨度划分为多个子区间，然后优化每个子区间的收敛控制参数，以达到较高的逼近精度。通过模拟和比较获得的解析解与其他传统的基于同伦的建模方法和数值分析求解的解，我们验证了 MuHAM 具有更高的 Quality Factor（引入以综合评估模型精度和计算成本），从而提高仿真效率。除了经典的 Hewlett-Packard (HP) RRAM 之外，还验证了一些当前的 RRAM。MuHAM 还具有支持定性和定量分析以及对收敛问题免疫的优势。它特别适用于其他具有强非线性的新型存储器件的解析建模。以及对收敛问题的免疫力。它特别适用于其他具有强非线性的新型存储器件的解析建模。以及对收敛问题的免疫力。它特别适用于其他具有强非线性的新型存储器件的解析建模。