A Theory of a Quartz Crystal Microbalance Based upon a Mason Equivalent Circuit

Abstract

The authors analyzed the behavior of a quartz crystal microbalance (QCM) in the experimental environments of air and liquid using a Mason equivalent circuit. It was found that the mass loading effect of QCM could be regarded as an inductance increase, and the analytical equation of the frequency shift, which is valid over the wide range of the thickness of a loading film, was derived. Utilizing this equation, the frequency shift can be predicted without solving the transcendental equation. Furthermore, it was found that various kinds of QCM problems, such as liquid loading and mass loading in liquid, could be solved using the same method because the acoustic load was expressed as a circuit component. Finally, the method to enhance mass loading sensitivity by depositing a thick film with low acoustic impedance over the quartz plate, was suggested.