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We generalize the two-dimensional scalar differential equations for thethickness-extensional operating modes of thin film bulk acoustic waveresonators (FBARs) to include the effects of surface impedance so that theequations can be used to model sensors based on FBARs. A mass sensor isanalyzed as an example to show the effectiveness of the equations obtained. Themass layer inducer frequency shifts are calculated. It is also found that thevibration may be confined under the driving electrode or the mass layer. Theseare fundamental to mass sensor design.

Scalar Differential Equations of Thin Film Bulk Acoustic Wave Resonators with Surface Acoustic Impedance for Sensor Application