Multi-parameter sensing using thickness shear mode (TSM) resonators – a feasibility analysis

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.