By C. Lu, A.W. Czanderna
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Extra info for Applications of Piezoelectric Quartz Crystal Microbalances
42). In practice, most QCMs involving large mass load allow only one side of the quartz crystal to receive the deposited material. In such cases, if the electrode on the other side is relatively thin, its effect is rather small and can be neglected. The final system consisting of deposited material and quartz crystal can then be adequately described by the model discussed in Sec. C. The fact that the effect of the back electrode is negligible was further demonstrated by the experimental results shown in Figs.
A convenient parameter to characterize the film-quartz combination is the acoustic imped ance ratio defined by Z - Zq/Zf (41) where Z q = (Pqiiq) % = PqVq, and Zf = (pfyf)1/z = PfVf are the charac teristic shear-mode acoustic impedances for unit cross sectional area of the quartz crystal and film, respectively. Using the definitions given for Z q and Zf, Eq. (30) becomes tan(7rfc/fq) = - ( 1 / Z ) tan(TTfc/ff). (42) Using the trigonometric identity tan [TT(fq - f c ) / f q ] = - tan (-rrf c /f q ) (43) and the definition of ff [Eq.
14) employed deposited films of considerable thickness. 5 mg/cm 2 onto a QCM in his experiments. 94 x 104 kg/m 3 ) for gold films. As the mass of deposited material becomes appreciable and forms a uniform layer of finite thickness, the assumption that acoustic waves do not propagate in the film becomes less accept able. In an effort to rectify the difficulties, Miller and Bolef  took a different approach and treated the quartz film combination as a composite acoustic resonator. The deposited film is considered as an integral part of the vibrating system.
Applications of Piezoelectric Quartz Crystal Microbalances by C. Lu, A.W. Czanderna