Electrode Effects in mmWave Frequency Multilayer Bulk Acoustic Wave Resonators

Abstract

<p>Electrodes are present in acoustic resonators to set electrical boundary conditions. Electrodes are acoustically part of a bulk acoustic wave (BAW) resonator that affect both its electromechanical coupling coefficient and its quality factor. Calculation of electromechanical coupling coefficient in multilayer structures requires the analysis of a system of equations relating the waves inside each layer to those in its adjacent layers. In this work, layer thicknesses and material constants in each layer are used to calculate the series and parallel resonance frequencies. Due to the proximity in frequency of series and parallel resonance, a series expansion of the series resonance frequency equation is performed around the parallel resonance frequency, and a closed form expression for electromechanical coupling coefficient from material constants and layer thicknesses is obtained to facilitate the observation of the electromechanical coupling coefficient effects of electrodes. Thermoelastic damping (TED) has been identified as the dominant acoustic loss mechanism in conductors. In this work, the complex wavenumber is calculated based on the unified theory of thermoelasticity to incorporate acoustic loss due to the interaction between elastic deformation and heat flow. 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 exists tradeoff among electromechanical coupling coefficient, acoustic quality factor, and electrical conductivity in the selection of electrode metals.</p>