title: Equivalent-circuit model for the thickness-shear mode resonator with a viscoelastic film near film resonance.
abstract: We derive a lumped-element, equivalent-circuit model for the thickness-shear mode (TSM) resonator with a viscoelastic film. This modified Butterworth-Van Dyke model includes in the motional branch a series LCR resonator, representing the quartz resonance, and a parallel LCR resonator, representing the film resonance. This model is valid in the vicinity of film resonance, which occurs when the acoustic phase shift across the film is an odd multiple of pi/2 rad. For low-loss films, this model accurately predicts the frequency changes and damping that arise at resonance and is a reasonable approximation away from resonance. Elements of the parallel LCR resonator are explicitly related to film properties and can be interpreted in terms of elastic energy storage and viscous power dissipation. The model leads to a simple graphical interpretation of the coupling between the quartz and film resonances and facilitates understanding of the resulting responses. These responses are compared with predictions from the transmission-line and Sauerbrey models.
authors.affiliation: Microsensor Research and Development Department, Sandia National Laboratories, Albuquerque, New Mexico 87185-1425, USA.
authors.forename: S J
authors.initials: SJ
authors.lastname: Martin
authors.forename: H L
authors.initials: HL
authors.lastname: Bandey
authors.forename: R W
authors.initials: RW
authors.lastname: Cernosek
authors.forename: A R
authors.initials: AR
authors.lastname: Hillman
authors.forename: M J
authors.initials: MJ
authors.lastname: Brown
mesh_terms: D004548:Elasticity; D017097:Electric Impedance; D004563:Electrochemistry / Q000295:instrumentation / Q000379:methods*; D004566:Electrodes; D011791:Quartz; D013499:Surface Properties; D014783:Viscosity
chemical_list: D011791:Quartz