Yoav Kessler

Bifurcation-based sensors, implementing stability boundaries monitoring in bistable microstructures, may manifest higher sensitivity and robustness when compared to their statically operated counterparts. In the operation of these devices, two key questions arise: 1) how to reliably identify the critical events associated with the transition between two stable states; 2) what is the maximal sampling rate allowing to identify these critical events in a periodically actuated device. Motivated by the potential implementation as a bifurcation-based flow sensor, in this work we experimentally explore the transient snap-through (ST) and snap-back (SB) dynamics of a bistable initially curved ( $500 \,\mu \text{m}$ long and $2.5\, \mu \text{m}$ wide) electrostatically actuated single-crystal Si microbeam. We employ a threshold-based approach for the ST and SB events detection and identify two mechanisms determining the maximal sampling frequency of the device: a phase lag between the voltage signal and the mechanical response and free decaying vibrations following the buckling event. In accordance with our experimental results and consistently with the reduced-order model predictions for the bistable beam operating at atmospheric pressure, at the actuation signal frequency of $\approx 0.6$ KHz, which is still much lower than the beam’s natural frequency of $\approx 110 $ KHz, the free oscillations engendered by one critical event (ST or SB) interfere with the consecutive one, preceding its emergence. On the other hand, an inherent phase lag ultimately hinders the abrupt ST and SB transitions at these actuating frequencies. [2021-0091]

We report on the fabrication and characterization of a generic, manufacturable, cantilever-type resonant sensing element, actuated by fringing electrostatic fields and fabricated from a silicon on insulator (SOI) wafer. The architecture of the electrode, designed to be thicker than the cantilever, was tailored to allow efficient electrostatic up-tuning of the beam's frequency and enhancement of the device frequency to voltage/displacement sensitivity in the initial “as fabricated” configuration. The device is not prone to undesired pull-in instability and can be operated at large deflections, which increases the dynamic range. The multilevel structure was fabricated using a two-stage critically timed deep reactive ion etching (DRIE). The device was operated statically and dynamically by a combination of dc and ac voltages, and an increase of the resonant frequency with the increasing voltage/deflection was registered. Consistently with the model predictions, the experimental results suggest that this type of sensing element can be promising for implementation in a large variety of resonant, inertial, force or pressure sensors.

An approach for gas flow velocity measurement at two different closely located points using a simple device incorporating only one thermal sensing element, is introduced and the feasibility to determine different velocities is experimentally demonstrated. An electrostatically actuated initially curved bistable microbeam heated by an electric current and convectively cooled by airflow is switched between two stable locations through the snap-through (ST) and snap-back (SB) buckling mechanisms. The velocities of an air flow at these positions are obtained by measuring the critical ST and SB values of the actuation voltage. In the experiments, our 500 μm long, 2 μm wide single-crystal Si beam with ≈ , 2.5,μm nominal initial elevation demonstrated sensitivity of SST ≈ 0.25 V/(m/s) and SSB ≈ 0.84 V/(m/s) at the ST and SB points, respectively. In the present device, the distance between the two measurement points is ≈10 μm. Our experimental results indicate that the suggested approach can be used for the velocity gradient measurements. The sensing principle relying on a single bistable sensing element opens new opportunities for measurement of gas flow velocity and velocity gradients at scales significantly smaller than the state-of-the-art multi hot-wire sensors.

Bistable microstructures demonstrate enhanced responsiveness to external stimuli in the vicinity of the critical configurations that separate stable and unstable states. This makes these devices attractive candidates for implementation in sensors. Here, after a short review of existing bistability-based sensing approaches, we explore the applicability of electrostatically and electro thermally actuated micro beams as flow sensors. Double clamped curved ≈ 1000 μ m long, ≈ 2.8μ m wide and ≈50 μ m thick beams, deep reactive ion etched (DRIE) from a silicon on insulator (SOI) wafer were subject to an air flow in the direction perpendicular to the beam. We show theoretically and experimentally that both the flow-induced cooling of the Joule's heated structure and the drag force reduce the critical snap-through (ST) voltages. The absolute and relative measured sensitivities of the ST voltage of ≈ 1.9 Vsm ^-1 and ≈ 2.6 % sm ^-1 , respectively, are consistent with the Reduced Order (RO) Galerkin model predictions.

We report on a How velocity measurement technique based on snap-through detection of an electrostatically actuated, bistable micromechanical beam. We show that induced elecro-thermal Joule heating, and the convective air cooling change the beam curvature and consequently, the critical snap-through voltage (V _ST ). Using single crystal silicon beams, we demonstrate the snap-through voltage to How velocity sensitivity of dV _ST /du ≈0.13 Vsm ^-1 with a power consumption of 360 μW. Our experimental results were in accord with the reduced order, coupled, thermo-electro-mechanical model prediction. We anticipate that electrostatically induced snap-through in curved, micromechanical beams will open new directions for the design and implementation of downscaled How sensors for autonomous applications and environmental sensors.

We explore both theoretically and experimentally the role of the flow direction on the performance of a novel flow sensor based on post buckling deflection monitoring of electro-thermally actuated double-clamped micro beams. Single crystal Si beams were buckled by a compressive stress arising due to Joule's heating. In the case of a flow directed along the beam, increase of the stream velocity resulted in decrease of the deflection due to the cooling of the beam by conductive heat transfer and convection. In the case of a transverse flow the drag force acting on the structure had a competing effect and deflection decrease was less pronounced. In the case of parallel flow, the deflection sensitivity of 1.5 μm/(m/s) and the critical current sensitivity of 0.4 mA/(m/s) were registered in the experiments. The results were qualitatively consistent with the predictions of the coupled nonlinear reduced order structural, fluidic and heat transfer models.

We report on a flow sensing approach based on deflection monitoring of a micro beam buckled by the compressive thermal stress due to electrothermal Joule's heating. The air stream, convectively cooling the device, affects both the critical buckling values of the electric current and the postbuckling deflections of the structure. After calibration, the flow velocity can be obtained from the deflection measurements. The quasi-static responses of 1000 μm and 2000 μm long, 10 μm wide, and 30 μm high single crystal silicon beams were consistent with the prediction of the model, which couples thermoelectric, thermofluidic, and structural domains. The deflection sensitivity of up to 1.5 μm/(m/s) and the critical current sensitivity of up to 0.43 mA/(m/s) were registered in the experiments. Our model and experimental results demonstrate the feasibility of the sensing approach and further suggest that simple, robust, and potentially downscalable beam-type devices may have use in flow velocity and wall shear stress sensors.