The analytical model of time-harmonic electric field and impedance spectrum in the multilayered interdigital electrode structure

Accurately determining the time-harmonic electric field and impedance spectrum in the multilayered interdigital electrode (IDE) transducers with lossy dielectrics is essential for the design of the structure, the property estimation of the dielectric, and performance optimization. This paper presents an analytical model of the electric field and impedance within a multilayered interdigitated electrode (IDE) when subjected to alternating excitation through the method of separation of variables (MSV). The equivalent circuit of IDE is established, where the impedance is the parallel of capacitive coupling and resistive coupling between electrodes. The general solutions for the electric field and impedance involving arbitrary numbers and complex permittivities of the dielectric layers are analytically derived. However, due to the approximation of boundary conditions, these physical quantities cannot be accurately obtained by the conventional analytical method using conformal mapping technique (CMT) and partial capacitance technique (PCT). The proposed model exhibits proficiency in generating precise electric field images and impedance values that closely correspond with simulated data, even when accounting for the frequency-dependent characteristics of permittivity and conductivity in lossy dielectrics. Moreover, the approaches to improve the sensitivity of a traditional three-layered IDE-based sensor are demonstrated. For a three-layered IDE-based capacitive sensor, improving the sensitivity can be accomplished through the incorporation of a ground plane at the substrate's bottom and increasing the metallization rate. Conversely, it is recommended to reduce the metallization rate, increase substrate thickness, and remove the ground plane in order to enhance the sensitivity of the IDE-based impedance sensor. The experimental results demonstrate that the proposed model generates outstanding impedance spectra (involving capacitance spectra and resistance spectra) results for various metallization ratios and top layers. This exemplifies the model's potential for predicting, designing, and enhancing a complex multilayered IDE-based transducer to achieve precise and sensitive detection.