Fully Three-Dimensional Analysis of TSM Quartz Sensors Immersed in Viscous Liquids

In order to optimize the design of piezoelectric thickness-shear-mode (TSM) liquid sensors, it is essential to understand the complete interaction between the resonator and the liquid. For instance, a major issue is the excitation of spurious, scarcely damped compressional waves, which can lead to disturbing interferences when reflected by nearby obstacles. Earlier attempts to model this effect include an approximation assuming a particular shear displacement distribution at the sensitive surface, and a finite element analysis, which turned out to be very time-consuming due to the large number of elements required. We present the first closed form and fully 3D analysis of the entire sensor-liquid interaction considering all wave modes. The analysis is based on a spectral-domain mode-expansion and yields the complete mechanical and electrical fields in the sensor and the liquid allowing the derivation of device characteristics such as the sensitivity and the equivalent circuit