Effective electromechanical coupling coefficient of high-overtone bulk acoustic resonator

A high-overtone bulk acoustic resonator （HBAR） is composed of a substrate, a piezoelectric film and upper and lower electrodes, the influences of their structure parameter （thickness） and performance parameter （characteristic impedance） on effective electromechani- cal coupling coefficient K^2eff are investigated systematically. The relationship between K^2eff and these parameters is obtained by a lumped parameter equivalent circuit instead of distributed parameter equivalent circuit near the resonant frequency, and K^2eff at the resonance frequency closest to the given frequency is analyzed. The results show that K^2eff declines rapidly and oscillatorily with the continuous increase of the substrate thickness when the piezoelectric film thickness is fixed, and decreases inversely proportion to the thickness when the substrate thick-ness is greater than a certain value. With the ratio of the characteristic impedance of the substrate to the piezoelectric layer increasing, the maximum of K^2eff obtained from the vari- ation curve of K^2eff with the continuous increase of the piezoelectric film thickness decreases rapidly before reaching the minimum value, and later increases slowly. Fused silica with low impedance is appropriate as the substrate of HBAR to get a larger K^2eff. Compared with Al electrode, Au electrode can obtain larger K^2eff when the appropriate electrode thickness is selected. The revealed laws above mentioned provide the theoretical basis for optimizing parameters of HBAR.

Mechanical quality factor of high-overtone bulk acoustic resonator

Mechanical quality factor Qm is a key characteristic parameter of High-overtone bulk acoustic resonator（HBAR）. The effects of structure parameter（thickness） and perfor？mance parameters（characteristic impedance and mechanical attenuation factor） of substrate,piezoelectric film and electrode constituting HBAR on Qm are carried out. The relationships between Qm and these parameters are obtained by a lumped parameter equivalent circuit instead of distributed parameter equivalent circuit near the resonance frequency, and the an？alytical expressions oi Qm are given. The results show that Qm increases non-monotonically with the continuous increase of the substrate thickness for HBAR with certain piezoelectric film thickness, and it approaches to the substrate material mechanical quality factor as the substrate thickness is large. Qm decreases wavily with the continuous increase of the piezoelectric film thickness for HBAR with certain substrate thickness. Sapphire and YAG with low mechanical loss are appropriate as the substrate to get a larger Qm- The electrode loss must be considered since it can reduce Qm- Compared with Au electrode, A1 electrode with lower loss can obtain higher Qm when the appropriate electrode thickness is selected. In addition, Qm decreases with the increase of frequency. These results provide the theoretical basis for optimizing the parameters of HBAR and show that trade-oflFs between Qm and must be considered in the design because their changes are often inconsistent.