Derivation of the shear compliance of thin films on quartz resonators from comparison of the frequency shifts on different harmonics: A perturbation analysis

Viscoelastic effects contribute to the shift in resonance frequency of quartz crystal resonators induced by deposition of thin films on the resonator surface. In turn, the mechanical stiffness of the film can be experimentally determined from a comparison of the resonance shifts on different harmonics. When the film is much thinner than the wavelength of shear sound, a series expansion of the viscoelastic effects to third order in film thickness leads to rather simple equations. When plotting the normalized frequency shift deltaf/f versus the square of the overtone order n(2) one finds a linear relationship, where the slope is determined by the film's elastic compliance. When the same analysis is carried out on the resonance bandwidths rather than the frequency shifts the viscous compliance is obtained. The effects of asymmetric coatings, electrodes, and liquid media are discussed. (C) 2001 American Institute of Physics.