Modeling tunable bulk acoustic resonators based on induced piezoelectric effect in BaTiO_3 and Ba_(0.25)Sr_(0.75)TiO_3 films

摘要

A model for tunable thin film bulk acoustic resonators (TFBARs) based on ferroelectric films is proposed. The model is based on electromechanical equations taking into account piezoelectric effect and electrostriction effect induced by the dc electric field. The dc field induced shift of the resonant frequency is explained by the high-order nonlinear effects in the ferroelectric material. The main contribution to the tunability of the resonant frequency under dc electric field can be attributed to electrostriction, which is nonlinear with respect to the mechanical deformation. It is shown that the upward or downward shift in the resonant frequency is given by the sign of the nonlinear component of the electrostriction tensor M. The model is verified by comparing the results with the measured microwave input impedance of BaTiO_3 and Ba_(0.25)Sr_(0.75)TiO_3 based TFBARs. For a positive sign of the nonlinear coefficient of electrostriction M, the model predicts an upward shift of the resonant frequencies (resonance and antiresonance) under dc biasing in case of the TFBAR based on BaTiO_3, whereas a negative sign of the nonlinear coefficient of electrostriction M predicts downward shift of the resonant frequencies for TFBAR based on Ba_(0.25)Sr_(0.75)TiO_3 films.