Electrode Effects in mmWave Frequency Multilayer Bulk Acoustic Wave Resonators

Electrodes are placed in acoustic resonators to set electrical boundary conditions, and they inevitably are acoustically part of the structure for a bulk acoustic wave (BAW) resonator that affect both its electromechanical coupling coefficient and its quality factor. In this work, a modal analysis is performed to obtain a closed-form expression for electromechanical coupling coefficient from material constants. The impact on electromechanical coupling coefficient effects due to the characterstic acoustic impedance of electrodes is observed in half wavelength per layer structures. Thermoelastic damping (TED) has been identified as the dominant acoustic loss mechanism in conductors. In this work, acoustic quality factors due to TED for common metals in  microelectromechanical systems (MEMS) processing are calculated to facilitate the observation of the quality factor effects of electrodes. It is observed that there are different strengths among characteristic acoustic impedance, acoustic quality factor, and electrical conductivity in different electrode metals.