Radial dependence of mass sensitivity for modified-electrode quartz crystal resonators

Quartz crystal resonators (QCR) with “modified electrode” geometries have been investigated as detectors in liquids and shown to have high sensitivity to the electrical properties of the load, caused by changes in the electrostatic capacitance. However, the ability of the crystal plate to have a stable vibration under the load is often impaired, due to the electrode geometry. In the present work, the mass sensitivity profile at the sensing surface is analytically calculated for various modified-electrode QCRs. The sensing surface is divided into a fully electroded, a partially electroded and an unelectroded region. The efficiency of each region is evaluated to determine possible design trade-offs for stable modified electrode QCRs. It is shown that, for some values of the electrode mass loading factor, the efficiency of the partially electroded region can be significant and thus must be accounted for as part of a stable sensing surface. Experimental measurements of the differential mass sensitivity were performed for a modified-electrode QCR and compared to theory