Analysis of vibrations coupling in mesa-shaped multi-channel quartz crystal microbalances

The principle of the QCM design is based on the energy trapping phenomena of the quartz. But under certain specific geometries of QCM, the energy trapping effect ratio will diminish abruptly and the measurement accuracy will be decreased appreciably under those geometries. In this study we used finite element method and the Mindlin beam theory to analyze the geometry under which such a phenomenon occurs. It is shown that the flexural wave is the main reason for the loss of energy trapping. We further discuss the wave decoupling ability of stepped mesa design and how this improves the characteristics of bi-mesa resonators. In the model of multi-channel QCM, the electrodes will interfere each other during operation and the measurement accuracy is reduced. Here, we applied the mesa design to the multi-channel QCM so that the energy trapping effect ratio could be increased. We further compared the efficiency between the conventional multi-channel QCM and the multi-channel QCM with mesa design.