Amal Z. Hajjaj

Experimental and analytical study of highly tunable electrostatically actuated resonant beams

We demonstrate theoretically and experimentally highly tunable clamped–clamped microbeam resonators actuated with electrostatic forces. Theoretically, the Galerkin procedure is used to solve for static deflection as well as the eigenvalue problem as a function of the dc voltage for different values of the ratio between the air gap and the thickness of the microbeam. We demonstrate theoretically and experimentally that the natural frequency of the microbeam can increase or decrease with the increase of the dc polarization voltage depending on the ratio between the air gap and the thickness. Hence, we show that unlike the classical softening effect of the dc voltage, by careful designs of the microbeams, the dc bias can be used to effectively increase the resonance frequencies by several factors. Experimental data are presented for two case studies of silicon beams showing the effective increase of their fundamental resonance frequencies by more than 50–80%. Excellent agreement is reported among the theoretical and experimental results.

Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters

We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.

Tunable Resonators for Nonlinear Modal Interactions.

Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.

Electrothermally Tunable Arch Resonator

This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of electrothermally actuated microelectromechanical arch beams. The beams are made of silicon and are intentionally fabricated with some curvature as in-plane shallow arches. An electrothermal voltage is applied between the anchors of the beam generating a current that controls the axial stress caused by thermal expansion. When the electrothermal voltage increases, the compressive stress increases inside the arch beam. This leads to an increase in its curvature, thereby increasing its resonance frequencies. We show here that the first resonance frequency can increase monotonically up to twice its initial value. We show also that after some electrothermal voltage load, the third resonance frequency starts to become more sensitive to the axial thermal stress, while the first resonance frequency becomes less sensitive. These results can be used as guidelines to utilize arches as wide-range tunable resonators. Analytical results based on the nonlinear Euler Bernoulli beam theory are generated and compared with the experimental data and the results of a multi-physics finite-element model. A good agreement is found among all the results. [2016-0291]

A scalable pressure sensor based on an electrothermally and electrostatically operated resonator

We present a pressure sensor based on the convective cooling of the air surrounding an electrothermally heated resonant bridge. Unlike conventional pressure sensors that rely on diaphragm deformation in response to pressure, the sensor does not require diaphragms of the large surface area, and hence is scalable and can be realized even at the nanoscale. The concept is demonstrated using both straight and arch microbeam resonators driven and sensed electrostatically. The change in the surrounding pressure is shown to be accurately tracked by monitoring the change in the resonance frequency of the structure. The sensitivity of the sensor, which is controllable by the applied electrothermal load, is shown near 57 811 ppm/mbar for a pressure range from 1 to 10 Torr. We show that a straight beam operated near the buckling threshold leads to the maximum sensitivity of the device. The experimental data and simulation results, based on a multi-physics finite element model, demonstrate the feasibility and simplicity of the pressure sensor. Published by AIP Publishing.

Tunable Bandpass Filter Based on Electrothermally and Electrostatically Actuated MEMS Arch Resonator

This paper demonstrates experimentally a wide bandpass filter based on an electrothermally tuned single MEMS arch resonator operated in air. The in plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC voltage is applied across the anchors to pass current through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting veiny close to the first resonance frequency. This leads to the phenomenon of veering, near crossing, where both modes exchange roles. Hence, the first resonance frequency becomes insensitive to axial forces and thermal actuation whereas the third resonance natural frequency becomes very sensitive. We demonstrate an exploitation of the veering phenomenon to realize a bandpass filter where the first and third resonance modes are excited electrostatically simultaneously to achieve a bandpass. We demonstrate also that by driving both modes nonlinearly near the veering regime, so that the first mode shows softening behavior and the third mode shows hardening behavior, sudden jumps in the response from both modes are induced leading to sharp roll off from the bandpass to the stop band. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.

Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators

We acknowledge the financial support of King Abdullah University of Science and Technology and Saudi Aramco.

Highly tunable NEMS shallow arches

We report highly tunable nanoelectromechanical systems NEMS shallow arches under dc excitation voltages. Silicon based in-plane doubly clamped bridges, slightly curved as shallow arches, are fabricated using standard electron beam lithography and surface nanomachining of a highly conductive device layer on a silicon-on-insulator wafer. By designing the structures to have gap to thickness ratio of more than four, the mid-plane stretching of the nano arches is maximized such that an increase in the dc bias voltage will result into continuous increase in the resonance frequency of the resonators to wide ranges. This is confirmed analytically based on a nonlinear beam model. The experimental results are found to be in good agreement with that of the results from developed analytical model. A maximum tunability of 108.14% for a 180 nm thick arch with an initially designed gap of 1 μm between the beam and the driving/sensing electrodes is achieved. Furthermore, a tunable narrow bandpass filter is demonstrated, which opens up opportunities for designing such structures as filtering elements in high frequency ranges.

Scalable Pressure Sensor Based on Electrothermally Operated Resonator

We experimentally demonstrate a new pressure sensor that offers the flexibility of being scalable to small sizes up to the nano regime. Unlike conventional pressure sensors that rely on large diaphragms and big-surface structures, the principle of operation here relies on convective cooling of the air surrounding an electrothermally heated resonant structure, which can be a beam or a bridge. This concept is demonstrated using an electrothermally tuned and electrostatically driven MEMS resonator, which is designed to be deliberately curved. We show that the variation of pressure can be tracked accurately by monitoring the change in the resonance frequency of the resonator at a constant electrothermal voltage. We show that the range of the sensed pressure and the sensitivity of detection are controllable by the amount of the applied electrothermal voltage. Theoretically, we verify the device concept using a multi-physics nonlinear finite element model. The proposed pressure sensor is simple in principle and design and offers the possibility of further miniaturization to the nanoscale.Copyright

Highly Tunable Narrow Bandpass MEMS Filter

We demonstrate a proof-of-concept highly tunable narrow bandpass filter based on electrothermally and electrostatically actuated microelectromechanical-system (MEMS) resonators. The device consists of two mechanically uncoupled clamped–clamped arch resonators, designed such that their resonance frequencies are independently tuned to obtain the desired narrow passband. Through the electrothermal and electrostatic actuation, the stiffness of the structures is highly tunable. We experimentally demonstrate significant percentage tuning (~125%) of the filter center frequency by varying the applied electrothermal voltages to the resonating structures, while maintaining a narrow passband of 550 ± 50 Hz, a stopband rejection of >17 dB, and a passband ripple ≤2.5 dB. An analytical model based on the Euler–Bernoulli beam theory is used to confirm the behavior of the filter, and the origin of the high tunability using electrothermal actuation is discussed.