Investigation of film-thickness determination by oscillating quartz resonators with large mass load

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Abstract
A one‐dimensional acoustical composite‐resonator model is used to study the behavior of a quartz‐crystal resonator with large mass load. On the basis of this model, it is found that the exact relationship between the frequency shift and the added mass depends on the acoustic impedance of the deposited material. The experimental data for three materials (silver, copper, and lead) with different acoustic impedances are shown to be in good agreement with the theoretical predictions. The validity and limitations of the presently used equations for thickness determination by quartz‐crystal resonators are also discussed.