Thermoelastic FEM-BEM model for Solidly Mounted Resonator

A Solidly Mounted Resonator (SMR) is an ultra-thin piezoelectric layer deposited between two electrodes which operates in longitudinal thickness mode. Minimization of dissipative losses is a major goal in SMR designs. For an accurate simulation of a SMR vibrating in vacuum, thermoelastic damping phenomenon related to the irreversible heat dissipation induced by the coupling between heat transfer and strain rate during the resonator vibration and acoustic radiation into the substrate have to be taken into account. The finite element method (FEM) is suitable for structural simulation, especially for thermoelastic damped structures vibrating in vacuum. When the vibrating structure is deposited on an unbounded elastic medium, the boundary element method (BEM) is suitable because it prescribes exact radiating conditions. Numerical FEM-BEM results are presented for an aluminum nitride resonator with molybdenum electrodes operating at 2.10 GHz and decoupled from the substrate by a tungsten-silicon dioxide or a silicon nitride-silicon oxycarbide Bragg reflector. Thermoelastic effect is shown to affect mainly SMR quality factor and temperature coefficient of frequency.