The Influence of Electrode on Elastic Constant $C_{33}{}^{D}$ Extraction of Scandium-doped Aluminum Nitride Thin Film by Thickness-extensional Mode FBAR

Recently, scandium-doped aluminum nitride $(\text{Sc}_{\mathrm{x}}\text{Al}_{1^{-}\mathrm{x}}\mathrm{N})$ has drawn a lot of attention as a promising material for RF-MEMS due to its large piezoelectric constants. In this paper we present the study of electrode effect on material constant extraction of $\text{Sc}_{\mathrm{x}}\text{Al}_{1^{-}\mathrm{x}}\mathrm{N}$ by measuring parallel resonant frequency of thickness-extensional mode thin film bulk acoustic resonator. Analytical method based on Mason model was adopted to investigate the effect of electrode material and thickness on the impedance spectrum of resonator. The accuracy of elastic constant $C_{33}{}^{D}$ extraction for ignoring the electrode was evaluated. The results show that electrode has a great effect on the impedance of resonator, a correction to electrode effect should be made for accurate extraction of $C_{33}{}^{D}$.