Model of ferroelectric FBARs including longitudinal and shear waves
Poster (konferens), 2011
In parallel-plate Film Bulk Acoustic Resonators (FBAR) the acoustic oscillations generated in the film due to the piezoelectric (including DC field induced) effect may consist of both thickness longitudinal and shear waves. The shear waves are generated mainly due to the c-axis tilted nanocolumns in the ferroelectric films. ADS and Mason based circuit model of a solidly mounted FBAR is proposed. Both thickness mode longitudinal and shear waves are taken into account. Since the shear and longitudinal waves are normal modes the resonator is represented as two independent longitudinal and shear wave resonators connected in parallel. For both resonators the thicknesses of the layers are given for longitudinal mode. The corresponding longitudinal and shear acoustic velocities, impedances and losses are used in longitudinal and shear resonators (“branches”). SiO2/W reflector and Ba0.25Sr1-xTiO3 film as the piezoelectric are assumed in simulations. The simulated reflector transmittivity, T=10•log(1-|S11|2), of the longitudinal and shear are shown in Fig.1. BSTO assumed to be infinite thick. Transmittivity of the shear modes is rather high. The relative power loss into the shear mode, Fig.2, is defined as 100•Pshear/(Plong+Pshers), %. In this case kt2long=0.013 and kt2shear=0.001. The fraction of the shear mode at longitudinal resonant frequency of 5.16 GHz is minimum (0.35%). This is due to lower resonant impedance of the longitudinal mode as compared with the shear mode which is off-resonance. The fraction of the shear mode increases with increasing shear mode coupling coefficient. Fig.3 compares measured and simulated performances of the resonator for kt2long=0.013 and kt2shear=0.001. These results are used to simulate/predict the performance of the resonator shown in Fig.4. The highest Q-factors of these resonances are achieved for certain coupling coefficients. The proposed ADS may be easily extended towards optimization of the Bragg reflector for efficient reflection of both longitudinal and shear modes.