An Investigation of Lateral Modes in FBAR Resonators.

Using first principles and the constitutive equations for a piezoelectric, we solve the 2D acoustic wave inside a single, infinite, piezoelectric membrane in order to study the dispersion of Thin Film Bulk Acoustic Resonator (FBAR) lateral modes, with and without infinitely-thin electrodes. The acoustic eigenfunction is a dual wave, composed of longitudinal and shear components, able to satisfy the 2D acoustic boundary conditions at the vacuum interfaces. For the single piezoelectric slab we obtain analytical expressions of the dispersion for frequencies near the longitudinal resonant frequency (Fs) of the resonator. These expressions are more useful for the understanding of dispersion in FBARs and more elegant than numerical methods like Finite Element Modeling (FEM) and various matrix methods. We additionally find that the interaction between the resonator's electrodes and the acoustic wave modifies the lateral mode dispersion when compared to the case with no electrodes. When correctly accounting for these interactions the dispersion zero is placed clearly at Fs, unlike what is calculated from a 2D model without electrodes where the dispersion zero is placed at Fp. This is important since all experimental evidence of measures FBAR resonators shows that the dispersion zero is at Fs. Furthermore, we introduce an electrical current flow model for the propagating acoustic wave inside the electroded piezoelectric and based on this model we can discuss an electrode-loss mechanism for FBAR lateral modes which depends on dispersion. From our model it results that lateral modes with real kx have higher electrode dissipation if they are closer to the resonant frequency. This is consistent with the typical behavior of measured FBAR filters where the maximum lateral mode damage on the insertion loss takes place for frequencies immediately below Fs.

Ultra-miniature coupled resonator filter with single-layer acoustic coupler.

Coupled resonator filters designed using a single-layer coupler require coupling materials with an acoustic impedance less than 5.0 MRayl. Carbon-doped oxide, with an acoustic impedance of 4.8 MRayl and an acoustic attenuation of 200 to 600 dB/cm at 1 GHz, can be used as a single-layer coupler to produce a competitive 2-stage coupled resonator filter for cellular handset applications in the gigahertz frequency range. The electrical response of our filter is superior to that of coupled resonator filters using a traditional acoustic mirror as the coupling element. We present an ultra-miniature 0.58 mm x 0.38 mm coupled resonator filter operating at a frequency of 2.15 GHz.