Thermoelastic damping modeling of a Si resonant beam with nanowire strain gauges

Resonant structures based on the combination of an electromechanical microresonator made in a thick single crystal Si layer and a differential piezoresistive detection with Si nanowires is a recent concept allowing a breakthrough in downscaling physical resonant sensors with equal to better performances. With an optimized design, the vacuum quality factor of these resonant structures will be ultimately limited by thermoelastic damping. Existing analytical models reasonably well predict the thermoelastic damping of transverse vibrations for beam resonators with and without axial stress but their limitations for resonators with more complex geometry is difficult to estimate. In this paper we investigate by Finite Element Method the effect of axial stress and of nanowire strain gages integration on the thermoelastic damping of vibrations of a beam resonator with a central inertial mass. Results show that axial stress effect depends on actuation force and that nanowires mainly alter the thermoelastic damping through an increase of resonator stiffness. As expected thermoelastic damping is reduced when torsional vibration modes are involved. Results are compared or analyzed with published analytical models.