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.