Analysis of the Radial Dependence of Mass Sensitivity for Modified-Electrode Quartz Crystal Resonators

Abstract

The radial dependence of mass sensitivity of the sensing surface is analytically calculated for two examples of “modified-electrode” quartz crystal resonators (QCR). The term “modified-electrode” QCR is used here with respect to the conventional QCR which has two identical circular and concentric electrodes. For these QCRs, the sensing surface is divided into a fully electroded, a partially electroded, and an unelectroded region, and the efficiency of each region is evaluated in terms of the electrode mass loading factor. Such QCRs are typically investigated for sensor applications in which the electrical properties of the liquid load or the coating deposited on the sensing surface (electroded and partially electroded regions) are being measured in addition to mass loading. While modified-electrode QCRs can be viewed as a simple capacitance sensor in those applications, the use of a piezoelectric crystal resonator in the narrow range of frequencies near resonance and antiresonance allows for a direct measurement of the capacitance through the antiresonant frequency, provided that the device damping (motional resistance) is not too high or that the resonance quality factor, Q, is high enough for a stable vibration under the load. It is shown that, for some values of the electrode mass loading factor, the off-electrode efficiency (partially electroded and unelectroded region efficiency) can still have a significant contribution to the overall surface area mass sensitivity. Knowledge of the efficiencies is needed to determine the loading area required for stable QCR sensor operation. This is because additional dissipation of energy into the load can occur, especially for cases where the sample load extends to the unelectroded surface, which has a nonnegligible particle displacement amplitude. It is also shown that, for some applications involving a liquid load and for some values of the electrode thickness, the shear particle displacement profile is such that compressional wave generation can contribute significantly to device damping, thus making the device unstable. Experimental measurements of the mass sensitivity profile on the surface are also performed for those QCRs and compared to theory.

Compressional acoustic wave generation in microdroplets of water in contact with quartz crystal resonators

“…As a consequence of the finite size of the electrodes, the translational disturbance amplitude, and hence sensitivity, is greatest at the center and decreases towards the perimeter in an approximately Gaussian fashion 3,4 .…”

Response of Quartz Crystal Microbalance Loaded with Single-drop Liquid in Gas Phase

“…Because of the symmetric electrode pattern, the device had high uniform mass sensitivity distribution [5][6][7].…”

Vibration optimization of ZnO thin film bulk acoustic resonator with ring electrodes

“…14,15 Therefore, a uniform displacement distribution is expected for high accuracy and repeatable measurements in sensor applications. Josse et al 16 once designed a ring electrode QCR and obtained obviously concave displacement profile and correspondingly a concave mass sensitivity curve. Gao et al 17 applied two methods of changing overtone order and designing electrode geometry, i.e., dot-ring and double-ring electrodes, to nearly eliminate the concavity of the displacement profile.…”