Influence of electrodes on the effective electromechanical coupling coefficient distributions of high-overtone bulk acoustic resonator

In this paper, the influence of the electrodes on effective electromechanical coupling coefficient k2eff distribution of high-overtone bulk acoustic resonators (HBAR) is investigated using the four-layer thickness extension mode composite resonator model. The k2eff distributions and the spacing of the parallel resonance frequency (SPRF) distributions are calculated for HBARs with different electrode and substrate materials. The frequency of first peak fM in k2eff distribution curve is close to the frequency of first valley in SPRF distribution curve, which has the maximum deviation of about 20%. The fM ratio of Al0.1μm-ZnO0.6μm-Au0.1μm-Sapphire400μm to Au0.1μm-ZnO0.6μm-Al0.1μm-Sapphire400μm is 1.91 which indicated that the k2eff distribution of HBAR is affected significantly by different electrode materials. We discuss for the first time the influence of the acoustic impedance ratio of the electrodes to substrate to the k2eff distribution, which is independent on the thickness ratio of the electrodes to piezoelectric film. It is found that for the pure-hard and pure-soft substrate HBARs, the resonator frequency of piezoelectric sandwich structure can be used to estimate the resonator frequency fM of the first peak of k2eff curve, which has the maximum deviation of 7%. The fabricated HBAR(I) Al-ZnO-Al-Sapphire and HBAR(II) Al-ZnO-Au-Sapphire shows identical outlines of k2eff and SPRF curves with the simulations, which have fMs of about 2 GHz and 3 GHz. The k2t of ZnO films are extracted from the first peak of the k2eff curve. The ZnO film deposited on Al and Au electrodes have k2t of 0.0597 and 0.0615, respectively.