The semi-analytical model of electric field and capacitance in a multilayer-structured interdigital electrode capacitor

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 η=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.