Abstract
Abstract. Multi-parameter sensing is examined for thickness shear mode (TSM) resonators that are in mechanical contact with thin films and half-spaces on both sides. An expression for the frequency-dependent electrical admittance of such a system is derived which delivers insight into the set of material and geometry parameters accessible by measurement. Further analysis addresses to the problem of accuracy of extracted parameters at a given uncertainty of experiment. Crucial quantities are the sensitivities of measurement quantities with respect to the searched parameters determined as the first derivatives by using tentative material and geometry parameters. These sensitivities form a Jacobian matrix which is used for the exemplary study of a system consisting of a TSM resonator of AT-cut quartz coated by a copper layer and a glycerol half-space on top. Resonant and anti-resonant frequencies and bandwidths up to the 16th overtone are evaluated in order to extract the full set of six material–geometry parameters of this system as accurately as possible. One further outcome is that the number of employed measurement values can be extremely reduced when making use of the knowledge of the Jacobian matrix calculated before.
Highlights
For many years thickness shear mode (TSM) resonators such as the quartz crystal microbalance (QCM) measuring systems are in use for direct recording of mechanically varying situations on a small geometric scale
We introduce the following abbreviations: Zq cq66,D vq the acoustic impedance of plate at the given electric displacement D, and τq the bulk acoustic waves (BAWs) propagation time through the plate
Equation (32) for the electrical admittance of acoustic pure shear waves propagating through a material system, as shown in Fig. 1, results in a specific periodicity caused by the trigonometric functions being contained
Summary
For many years thickness shear mode (TSM) resonators such as the quartz crystal microbalance (QCM) measuring systems are in use for direct recording of mechanically varying situations on a small geometric scale. The peak frequency (resonant frequency) is shifted under the influence of changed boundary conditions at the plate surface, such as the case at the deposition of a thin layer or at an impact of an adjacent fluidic (gaseous and liquid) medium on one or both plate surfaces. Just these plausible exemplary situations have been crucial for the first relevant publications on this matter by Sauerbrey (1959) and King Jr. We define the FWHM of anti-resonance as the difference of frequencies belonging to one-half of the squared maximum of impedance amplitude
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