Extraction of Electromechanical Coupling Coefficient of Film/Substrate Structure by Using the Ratio of a Third Mode Resonant Frequency to a Fundamental Mode Resonant Frequency

The electromechanical coupling coefficient k-{\text{t}^{2}} is an important parameter for determining the bandwidth and insertion loss of the RF filters. A resonance antiresonance method is recommended for the determination of k-{\text{t}^{2}} for the piezoelectric film, according to IEEE standard. However, a self-standing film structure (FBAR) is required to use this method. It is convenient to estimate the k-{\text{t}^{2}} of piezoelectric film in film/substrate structure (HBAR) before the FBAR process. In this study, we propose a new k-{\text{t}^{2}} determination method by using the ratio of a third mode resonant frequency to a fundamental mode resonant frequency in HBAR without removing the substrate.