Abstract—

Models that describe bipolar resistive switching (BRS) in planar microstructures based on oxide compounds (Bi₂Sr₂CaCu₂O_{8 + x} and Nd_{2 – x}Ce_xCuO_{4 – y}) and bismuth selenide are considered. Metal/insulator/metal planar-type memristor heterostructures in which the microsize is formed by an electrode with a diameter much smaller than the total size of the structure (which can be both Sharvin-type microcontacts and film electric electrodes) are investigated. Another important feature of these heterostructures is the presence of a surface layer several tens of nanometers thick with the specific conductivity significantly reduced relative to the bulk conductivity. The change in the resistive properties of such heterostructures is caused by the formation or destruction of a conducting channel through the mentioned layer. Numerical simulation has shown that the BRS is significantly affected by the topology of the electric field’s distribution. To describe the experimentally observed memristor effects in the investigated heterostructures, a model of a critical field is proposed. In this model it is assumed that the change in the specific conductivity occurs in those parts of the surface layer where the electric field strength exceeds some critical value. The critical field model is based on the numerical calculation of the electrical potential distribution from the distribution of the specific conductivity in the structure. In addition, a model that enables analysis of the influence of the electrodiffusion of oxygen ions on resistive switching in the heterostructures based on Bi₂Sr₂CaCu₂O_{8 + x} is considered. In the numerical realization of the models, a combination of the integrodifferential approximation of differential equations, the multigrid approach for localization of heterogeneities in physical characteristics, the iterative decomposition method, and the composite adaptive meshes are used. This allows tracking the investigated processes with the necessary accuracy. The simulation results are compared with the experimental data.

中文翻译：

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数值模拟在基于氧化物和硫属元素化物的忆阻器结构研究中的应用

摘要—

基于氧化物（Bi ₂ Sr ₂ CaCu ₂ O _{8 + x}和Nd _{2 – x} Ce _x CuO _{4 – y}）的平面微结构中描述双极电阻转换（BRS）的模型）和硒化铋。研究了金属/绝缘体/金属平面型忆阻器异质结构，其中的微细尺寸是由直径远小于结构总尺寸的电极形成的（可以是Sharvin型微接触和薄膜电电极）。这些异质结构的另一个重要特征是存在几十纳米厚的表层，其比电导率相对于体电导率显着降低。这种异质结构的电阻特性的变化是由穿过所述层的导电通道的形成或破坏引起的。数值模拟表明，BRS受电场分布拓扑的影响很大。为了描述在所研究的异质结构中实验观察到的忆阻器效应，提出了临界场模型。在该模型中，假设电导率的变化发生在表面层中电场强度超过某个临界值的部分。临界场模型基于结构中比电导率分布的电势分布的数值计算。此外，基于Bi的模型可以分析氧离子的电扩散对异质结构中电阻转换的影响 在该模型中，假设电导率的变化发生在表面层中电场强度超过某个临界值的部分。临界场模型基于结构中比电导率分布的电势分布的数值计算。此外，基于Bi的模型可以分析氧离子的电扩散对异质结构中电阻转换的影响 在该模型中，假设电导率的变化发生在表面层中电场强度超过某个临界值的部分。临界场模型基于结构中比电导率分布的电势分布的数值计算。此外，基于Bi的模型可以分析氧离子的电扩散对异质结构中电阻转换的影响_考虑2 Sr ₂ CaCu ₂ O _{8 + x}。在模型的数值实现中，使用了微分方程的积分微分逼近，物理特性异质性局部化的多重网格方法，迭代分解方法和复合自适应网格。这样可以以必要的精度跟踪调查的过程。仿真结果与实验数据进行了比较。