Abstract
We studied mode couplings in thin film bulk acoustic wave resonators of a piezoelectric film on a dielectric layer operating with the fundamental thickness-extensional mode. A system of plate equations derived in our previous paper was used which includes the couplings to the unwanted in-plane extension, flexure, fundamental and second-order thickness shear modes. It was shown that the couplings depend strongly on the plate length/thickness ratio. For a relatively clean operating mode with weak couplings to unwanted modes, a series of discrete values of the plate length/thickness ratio should be avoided and these values were determined in the present paper. The results can be of great significance to the design and optimization of film bulk acoustic wave resonators.
Highlights
Acoustic wave resonators made from piezoelectric crystals are key components of electrical circuits called oscillators in a lot of electronic equipment.[1,2] As frequency standards, resonators are widely used for time keeping, frequency operation, and signal generation and processing
In this paper we study the most common FBARs in which the c-axis of the piezoelectric films are in the plate thickness direction and the FBARs operate with the fundamental thickness-extensional mode of the plates
The geometric parameters are determined by hf = 15 μm, hs = 5 μm, h = 0.2 μm, R = ρ h /(ρf hf ) = 0.01. For such an FBAR, the correction factors were determined in Ref. 26 by matching the dispersion relations of the relevant coupled waves calculated from both the plate equations and the three dimensional equations.[27,28]
Summary
Acoustic wave resonators made from piezoelectric crystals are key components of electrical circuits called oscillators in a lot of electronic equipment.[1,2] As frequency standards, resonators are widely used for time keeping, frequency operation, and signal generation and processing. Theoretical modeling of mode couplings in FBARs is crucial to the current design and manufacturing of FBARs. In our previous paper,[26] a system of two-dimensional equations for the operating thicknessextensional mode with couplings to the relevant spurious modes was derived. The spurious modes included in Ref. 26 are the in-plane extensional mode, the flexural mode, the fundamental thicknessshear mode, and the second-order thickness-shear mode. These are the modes that are coupled to the operating thickness-extensional mode in the frequency range of interest of FBARs. In Ref. 26, the propagation of these coupled waves in unbounded plates was studied to verify the equations obtained and determine the correction factors in the equations. In this paper we use the equations obtained in Ref. 26 to analyze the couplings between the operating mode and the spurious modes in a finite plate FBAR
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