Q-factor and frequency shift of resonating silicon diaphragms in air

The dependence of the relative frequency shift and the Q-factor of the first two modes of vibration of square silicon diaphragms on the diaphragm geometry and the air pressure is investigated. The experimental results are compared with the theory, which is based on Lamb's theory for circular diaphragms. It assumes acoustic radiation to be the determining mechanism for the energy loss of the diaphragm. The experimental results for both the frequency shift and the Q-factor as a function of the pressure deviate from the theory. A possible explanation for this deviation is the assumption that viscous damping plays an important role. It is found that the vibrating diaphragm is able to put the whole wafer into vibration, which causes several interfering effects. This phenomenon limits the applicability of vibrating diaphragms in resonant sensors.