Analytical and experimental study on the second harmonic mode response of a bulk acoustic wave resonator

A one-dimensional Mason model is employed to investigate the second harmonic mode response of a multilayer composite film bulk acoustic resonator (FBAR), particularly the dependence of the effective coupling coefficient (K_{t, eff}²) on material properties and relative position in the acoustic stack. The simulation results for AlN-based FBAR with electrode layer having relatively low acoustic impedance and additional temperature compensation layer reveals that the maximum values of K_t,eff ²are obtained with a thickness ratio (between the non-piezoelectric layer and piezoelectric layer) that is close to its acoustic velocity ratio. The fundamental mode and second harmonic mode operation of an FBAR are compared. The maximum achievable K_t,eff² is comparable (5.39% versus 5.16%) for the temperature compensated FBAR (with Mo as electrodes) operating at fundamental and second harmonic modes. However, the trimming-mass and crossover temperature sensitivities of the second harmonic mode are lower, indicating its potential advantage over the fundamental mode for high frequency applications above 2 GHz (such as filters, low phase noise temperature stable oscillator applications). Experimental results on a ZnO-based FBAR (Al/ZnO/Al/SixNy) operating around 5 GHz with various thicknesses of ZnO and SixNy show good agreement with numerical modeling.