MEMS Beam Research Articles

Strong coherent energy exchange induced by the bending-bending mode-coupling effect in doubly clamped MEMS beam resonators

Strong coherent energy exchange induced by the bending-bending mode-coupling effect in doubly clamped MEMS beam resonators

Multiphysics Coupling Model of Flexible Multisensor System Based on MEMS Beam Structure

Multiphysics Coupling Model of Flexible Multisensor System Based on MEMS Beam Structure

Deep Learning for Nonlinear Characterization of Electrostatic Vibrating Beam MEMS

In this paper, we integrate deep learning techniques with the motion-induced current method to analyze the nonlinear response of electrostatic MEMS resonators consisting of vibrating beams under electrostatic actuation. The motion-induced current method relies on a transduction mechanism that converts the motion of the resonator to a current signal. The third harmonic of the induced current captures the motion characteristics of the MEMS resonator. We conduct electrical measurements on a MEMS device comprising a microcantilever beam subject to electrostatic actuation using a side electrode. The electrical measurements are verified against their optical counterparts to confirm the suitability of the motion-induced current method to analyze the motion of the MEMS resonator. Next, we develop a model by combining deep learning methods with experimental data aiming to detect the nonlinear dynamics associated with the motion of the resonator when subjected to large actuation voltages. The results demonstrate high prediction accuracy of the data-driven model in terms of capturing the peak resonance, the onset of bifurcation, the occurrence hysteresis and its bandwidth.

Nano/micro-beam deflections: Investigation of subjected forces and applications

Micro- and Nano beam MEMS devices possess a broad range of applications owing to their capability to produce precise mechanical motion and sensing capabilities at a small scale. In the field of biomedicine, these devices have been employed in applications such as tissue engineering, lab-on-a-chip systems, and implantable devices. Medical devices, particularly those involved in drug delivery, are significantly impacted by the forces applied to them. Therefore, it is imperative to carefully evaluate the effects of axial force and optimize the device's design to ensure that it can endure the forces it will encounter during operation. Despite being relatively weak, the van der Waals force warrants careful consideration when working at the micro- and nanoscales. In this research, the nonlinear equation obtained by the Galerkin method for a doubly clamped nano/micro-beam under the effect of Van der Waals (vdW) force was solved. The Homotopy Perturbation Method (HPM) and the Akbari Ganji Method (AGM) are introduced to investigate the nonlinear problem in this paper analytically. To validate and investigate the accuracy of the AG and HP methods, the obtained results were compared to the Runge-Kutta approach. The obtained results for all data sets showed the high accuracy of the AG and HP methods. Also, this paper investigated the effect of axial force N on beam type N/MEMS deflection. The axial force N effect in both tensional (N > 0) and compressive (N < 0) modes has been investigated. Due to the obtained results, increasing the axial force compressively increases the deflection of the beam. However, this trend is reversed for the tensional axial force.

The combined effects of temperature and relative humidity on resonant frequency and quality factor of MEMS beam resonators in atmospheric pressure and gas rarefaction

The combined effects of temperature and relative humidity on resonant frequency and quality factor of MEMS beam resonators in atmospheric pressure and gas rarefaction

Mechanical Control of Nonlinearity in Doubly Clamped MEMS Beam Resonators Using Preloaded Lattice-Mismatch Strain

We theoretically clarify the mechanism of the strain-tuning effect for control of the mechanical nonlinearity in doubly clamped MEMS beam resonators and experimentally demonstrate that nonlinearity can be effectively suppressed with a preloaded lattice-mismatch strain in the MEMS beam. Mechanical nonlinearity arises from the hardening- and softening-nonlinearity terms in the Duffing motion equation of the MEMS beam. By approaching the buckling condition of the MEMS beam, the substantially increased softening nonlinearity greatly compensates for the hardening nonlinearity, resulting in suppression of the total nonlinearity. Utilizing this knowledge, we fabricate ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ MEMS beams with a preloaded lattice-mismatch strain, which is achieved by adding a small amount (x = \ensuremath{\sim}0.4%) of indium to the $\mathrm{Ga}\mathrm{As}$ MEMS beam during wafer growth. The buckling condition in the experiment is achieved by carefully modulating the length of the ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ MEMS beams. As a result, mechanical nonlinearity is largely modulated from hardening to softening and reaches a quasizero value near the buckling condition, demonstrating the effectiveness of using lattice mismatch for controlling the mechanical nonlinearity of MEMS resonators.

Knudsen force based double beam MEMS vacuum pressure sensor

Knudsen forces are gas molecular forces, generated due to the presence of a thermal gradient between two surfaces in rarefied gas and can be effectively used for the measurement of low pressures. This work reports on a Knudsen force based micro electro mechanical systems low pressure sensor consisting of two stacked beams of polysilicon—one acting as a heater while the other as a sensor. The structure is fabricated using a double sacrificial layer surface micromachining process. The thermal gradient across the two stacked beams is induced by resistive heating of the heater beam. The effect of using two separate beams for heating and sensing has been investigated at different heater current and the results are compared with the existing works. The provision of two beams has resulted in the sensor functioning at very low pressure of less than 0.1 Pa with an improved sensitivity of 15.5 fF mPa−1.

Design and Analysis of a Hybrid-Type RF MEMS Phase Detector in X-Band.

In this paper, we have designed, analyzed, and characterized a hybrid-type MEMS device for X-band phase shift measurement. The signal related to a phase shift of the inputs is fractionally in-line coupled by a MEMS beam and delivered to a thermoelectric power sensor, where the phase is ultimately converted into DC voltage output. With the hybrid of the MEMS beam and the thermoelectric power sensor, both in-line detection process and phase-DC voltage conversion is reserved, which is a benefit for large power capacity, good linearity property, and high-level integration density. In order to get a deep insight into the physical mechanisms involved in the phase detection process, a comprehensive analysis model is presented. The beam is modeled as a precise RLC circuit component, where the capacitance is related to the input power. The fabrication is compatible with GaAs monolithic microwave integrated circuit (MMIC) technology. Experimental results show that return loss is smaller than −11.3 dB and isolation is better than −9.3 dB over X-band. Phase shift detection from 0 to 180 degrees is verified for a large power range of 200–1600 mW (23–32 dBm). The perfect linearity property of the phase-detection sensitivity is demonstrated in the same power range. Low intermodulation distortion is also confirmed through measurement. It is revealed from the comparison between this work and other published results in the literature that this presented hybrid-type structure shows superiorities in both power handling ability and phase-detection linearity. It can be adopted in medium power signal applications with a high level of integration.

A 10-MHz FREE-FREE BEAM MICROMECHANICAL RESONATOR FABRICATION PROCESS USING SURFACE-MICROMACHINED TECHNOLOGY

The fabrication process for the designed MEMS resonator using surface-micromachined technology is presented in this paper. A 10-MHz Free-Free beam MEMS resonator is designed to vibrate in the second-mode shape, which is significant improvement compare to the fundamental mode. The design showed a Q value as high as 75,000, which is significant improvement compared to 8,400 VHF F-F beam MEMS resonator by K. Wang; and very low motional resistance (18kΩ). The surface-micromachined technology is used as the standard process for the design. The process is briefly described from the layout design to the experimental fabricated device.

1J1-3 Relationship between MEMS Mirror Angle and Beam Characteristics in High-Speed Scanning Ultrasound Microscopy

1J1-3 Relationship between MEMS Mirror Angle and Beam Characteristics in High-Speed Scanning Ultrasound Microscopy

Thermal tuning of mechanical nonlinearity in GaAs doubly-clamped MEMS beam resonators

We report the thermal tuning of the mechanical nonlinearity in GaAs double-clamped MEMS beam resonators for sensitive thermal sensing applications. We have estimated the mechanical nonlinearity in GaAs MEMS beam resonator by measuring its resonance frequency as a function of oscillation amplitude. The MEMS resonator shows a hardening nonlinearity with a small linear oscillation range of ∼30 nm. When electrical heat is applied to the MEMS beam, we have observed a significant reduction in the mechanical nonlinearity of MEMS resonators near the buckling point of the MEMS beam. The decrease in the mechanical nonlinearity originates from the bending of the MEMS beam, which gives a softening nonlinearity term and, hence, compensates the total nonlinearity. With the thermal tuning effect, MEMS resonator can maintain a very large quasi linear oscillation amplitude of ∼300 nm, which is ∼10 times larger than the linear oscillation range without the control of nonlinearity.

GaAs-based microelectromechanical terahertz bolometers fabricated on high-resistivity Si substrates using wafer bonding technique

We have fabricated GaAs-based microelectromechanical systems' (MEMSs) terahertz bolometers on high-resistivity Si substrates by using a wafer-bonding technique. In contrast to polar GaAs, nonpolar Si has very small absorption in the terahertz (THz) frequency range. The wafer-bonded MEMS bolometers show a large responsivity even in the Reststrahlen band of GaAs, where the responsivity vanishes in the conventional MEMS bolometers fabricated on GaAs substrates. Furthermore, we have observed two peaks in the responsivity spectrum near the TO and LO phonon frequencies of GaAs, which originate from an interplay between strong reflection in the Reststrahlen band and strong absorption at the TO phonon frequency in the GaAs MEMS beam. The present result demonstrates that the wafer-bonded MEMS bolometers are a very good candidate for the room-temperature, fast, and sensitive broadband THz detection.

Fabrication and function examination of PZT-based MEMS accelerometers

In this study, a hybrid sol-gel method was used to fabricate Pb(Zr0.52Ti0.48)0.98Nb0.02O3 (PNZT) piezoelectric thick films. By preparing Pb(Zr0.52Ti0.48)0.98Nb0·02O3 sol-gel solutions and mixing them with PZT-5A piezoelectric powders, therefore, the thickness of single layer coating can be increased and reduce the risk of film cracks. The proposed PNZT films have the dielectric constant of 1750, dielectric loss of 0.063, remnant polarization of 58 μC/cm2, and d33 of 133 p.m./V. Piezoelectric cantilever beam MEMS accelerometers were then designed, simulated and fabricated via photolithography methods on Si substrates. The sensitivity and natural frequency of the cantilever beam accelerometer are 16.8 mV/g and 200Hz, respectively. Finally, a cantilever beam accelerometer is successfully applied for the server hard-drive fault detection.

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

This work investigates the dynamics of a microbeam-based MEMS device in the neighborhood of a 2:1 internal resonance between the third and fifth vibration modes. The saturation of the third mode and the concurrent activation of the fifth are observed. The main features are analyzed extensively, both experimentally and theoretically. We experimentally observe that the complexity induced by the 2:1 internal resonance covers a wide driving frequency range. Constantly comparing with the experimental data, the response is examined from a global perspective, by analyzing the attractor-basins scenario. This analysis is conducted both in the third-mode and in fifth-mode planes. We show several metamorphoses occurring as proceeding from the principal resonance to the 2:1 internal resonance, up to the final disappearance of the resonant and non-resonant attractors. The shape and wideness of all the basins are examined. Although they are progressively eroded, an appreciable region is detected where the compact cores of the attractors involved in the 2:1 internal resonance remain substantial, which allows effectively operating them under realistic conditions. The dynamical integrity of each resonant branch is discussed, especially as approaching the bifurcation points where the system becomes more vulnerable to the dynamic pull-in instability.

Two-to-one internal resonance in the higher-order modes of a MEMS beam: Experimental investigation and theoretical analysis via local stability theory

The present study is focused on the dynamics of a microbeam-based MEMS device and analyzes its behavior in the neighborhood of the third natural frequency. An extensive experimental investigation is conducted. The main resonant and non-resonant branches span a wide range of coexistence. The 2:1 internal resonance is activated between the third and fifth modes, in which case the device exhibits complex and intriguing dynamics. The experimental data are examined in depth using various analytical and numerical tools. Alongside with the experiments, theoretical simulations are developed, where the main features of the internal resonance are properly represented and the contribution of each mode is discussed. The main steps of the progression of the 2:1 internal resonance are highlighted and the possibility of more complex internal resonances is explored, where different higher modes are involved.

1:1 internal mode coupling strength in GaAs doubly-clamped MEMS beam resonators with linear and nonlinear oscillations

We have investigated the 1:1 internal mode coupling strength in a GaAs doubly-clamped MEMS beam resonator by thermally tuning the frequencies of two neighbored resonant modes. The anti-crossing of the resonant frequencies indicates that the two modes couple with each other, and the mode coupling strength was estimated by the splitting of the anti-crossed frequencies of the two modes. When the oscillation amplitudes were tuned from the weakly-driven linear regime to the strongly-driven nonlinear regime, we observed slightly increased frequency splitting, indicating that the nonlinear oscillation only makes a very small contribution to the mode coupling strength.

Micro beam MEMS sensor for micro gas chromatography

Micro beam MEMS sensor for micro gas chromatography

Giant Enhancement in the Thermal Responsivity of Microelectromechanical Resonators by Internal Mode Coupling

We report on a giant enhancement in the thermal responsivity of the doubly-clamped GaAs microelectromechanical (MEMS) beam resonators by using the internal mode coupling effect. This is achieved by coupling the fundamental bending mode with the fundamental torsional mode of the MEMS beam resonators through the cubic Duffing nonlinearity. In the mode coupling regime, we have found that, when the input heat to the MEMS resonators is modulated at a particular frequency, the resonance frequency shift caused by heating can be enhanced by almost two orders of magnitude. The observed effect is promising for realizing high-sensitivity thermal sensing by using MEMS resonators, such as ultrasensitive terahertz detection at room temperature.

A vibrating beam MEMS accelerometer for gravity and seismic measurements

This paper introduces a differential vibrating beam MEMS accelerometer demonstrating excellent long-term stability for applications in gravimetry and seismology. The MEMS gravimeter module demonstrates an output Allan deviation of 9 μGal for a 1000 s integration time, a noise floor of 100 μGal/√Hz, and measurement over the full ±1 g dynamic range (1 g = 9.81 ms−2). The sensitivity of the device is demonstrated through the tracking of Earth tides and recording of ground motion corresponding to a number of teleseismic events over several months. These results demonstrate that vibrating beam MEMS accelerometers can be employed for measurements requiring high levels of stability and resolution with wider implications for precision measurement employing other resonant-output MEMS devices such as gyroscopes and magnetometers.

Characterisation of the internal resonances of a clamped-clamped beam MEMS resonator

Nonlinear coupling between modes through internal resonance has many applications in MEMS resonators. The primary objective of this work is to systematically study all possible internal resonance conditions between the first three modes and the feasibility of mode interaction in an electrostatically excited, straight, clamped-clamped beam. The static displacement and the first three natural frequencies of the beam are obtained for an applied DC voltage by using Galerkin based reduced order model and finite element method. All six possible commensurable relations between the first three frequencies of the beam are obtained by sweeping the non-dimensional parameters ($$\alpha _1$$ and $$\alpha _2 V_\mathrm{dc}^2$$) which depend on beam dimensions, material properties and external forcing. It is also demonstrated by a further examination of the dynamical equations that only one resonance condition is capable of exhibiting modal coupling when externally excited. A detailed analysis is carried out for this feasible resonance condition by altering $$\alpha _1$$ and $$\alpha _2 V_\mathrm{dc}^2$$ and solving the relevant nonlinear coupled equations by using both numerical time integration and the method of multiple scales. From this study, we observe that the lower mode is automatically excited after driving amplitude for the higher mode reaches a critical value—a sign of mode interaction initiation. We also find that amplitude of the higher mode is saturated after interaction with the lower mode for a combination of $$\alpha _1$$ and $$\alpha _2 V_\mathrm{dc}^2$$. Moreover, we see that the frequency bandwidth of modal interaction increases with excitation amplitude for all combinations of $$\alpha _1$$ and $$\alpha _2 V_\mathrm{dc}^2$$. Finally, the role of external damping on the amplitude-frequency response curve of both modes during the mode interaction is also investigated.