Accurately determining the electric field and capacitance in multilayer-structured interdigital electrode capacitor (IDC) transducers is an important prerequisite for designing the structure, estimating properties, and optimizing performance. In this paper, a semi-analytical model of the electric field and capacitance in a multilayered IDC is introduced utilizing the method of separation of variables. The general solutions for the field and capacitance, considering arbitrary numbers and permittivities of the dielectric layers, are analytically expanded in infinite series form, while these physical quantities cannot be accurately obtained by the traditional analytical model that employs the conformal mapping technique and the partial capacitance technique with boundary condition approximations at the dielectric interface. The proposed model with the recommended number of expanded terms successfully generates precise electric field images and capacitance values agreeing well with simulated data, even when there is a significant difference in the permittivity of adjacent layers. Moreover, based on the model, it can be concluded that the sensing range, referred to as the penetration depth, of a three-layer-structured IDC sensor, peaks at the optimal metallization ratio of =0.5 regardless of the permittivity and the number of electrodes. Experimental results demonstrate that the proposed model yields outstanding capacitance outcomes across different metallization ratios and various upper layers. This showcases the model's potential for designing and optimizing an IDC transducer for precise sensitive detection.

中文翻译：

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多层结构叉指电极电容器电场和电容的半解析模型


准确确定多层结构叉指电极电容器（IDC）换能器中的电场和电容是设计结构、评估特性和优化性能的重要前提。本文利用变量分离的方法介绍了多层 IDC 中电场和电容的半解析模型。考虑任意数量和介电层的介电常数，场和电容的一般解被解析展开为无限级数形式，而这些物理量无法通过采用共形映射技术和部分电容的传统解析模型精确获得介电界面处的边界条件近似技术。即使相邻层的介电常数存在显着差异，具有推荐数量的扩展项的所提出的模型也成功地生成了与模拟数据非常吻合的精确电场图像和电容值。此外，根据该模型可以得出结论，无论介电常数和介电常数如何，三层结构IDC传感器的传感范围（即穿透深度）在最佳金属化率=0.5时达到峰值。电极。实验结果表明，所提出的模型在不同的金属化比率和各种上层上产生了出色的电容结果。这展示了该模型在设计和优化 IDC 传感器以实现精确灵敏检测方面的潜力。