Squeeze Film Damping by a Structured Cavity in an AIr-Coupled Electrostatic Ultrasonic Transducer

Recently Monsalve et al. presented an electrostatic air-coupled ultrasonic transducer based on laterally moving beams (L-cMUT). In contrast to pMUTs and cMUTs, the device structure utilizes the chip volume to generate ultrasound in the kHz-frequency range, where absorption losses are small. Main advantages of the CMOS-compatible device are the low driving voltages combined with a broadband response. Possible applications are gesture recognition, ultrasonic imaging or range finding. Here, each beam is actuated by a stator. A periodic change of the cavity volume between beam and stator generates the pressure signal. Thereby, a smaller gap between both leads to higher electrostatic driving forces but simultaneously increases damping. Too small gaps may lead not only to a high damping but also to the pull-in effect for which the electrostatic force exceeds the restoring elastic force and the beam touches the stator producing a shortcut. For a successful design process, a precise model including elastic, electrostatic as well as damping effects is crucial. Too small damping carries the risk of instabilities like frequency jumps or a parametrically induced pull-in. High damping reduces the achievable deflection as well as the accessible frequency range. Previously, the static deflection was modelled with high accuracy by the beam's zero mode while the Q-factor was determined only experimentally. Thereby, a stator exhibiting the shape of the beam's zero mode reduces the pull-in voltage. The structured cavity further affects the squeeze-film damping between beam and stator. Here, we show how to use the Chebyshev-Edgeworth approach proposed by Schenk et al. to describe the damping with a single-degree of freedom model. The analytic expressions are compared with a modal FEM analysis. In summary, the structured stator improves not only the pull-in voltage but also lowers the squeeze-film damping.