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

TL;DR

This paper extends scalar differential equations for thin film bulk acoustic wave resonators to include surface impedance effects, enabling improved modeling of sensors like mass sensors and analyzing vibration confinement.

Contribution

It introduces generalized equations incorporating surface impedance for FBARs, aiding in the design and analysis of acoustic sensors.

Findings

Frequency shifts due to added mass are calculated.

Vibration confinement can occur under electrodes or mass layers.

The equations effectively model sensor behavior.

Abstract

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