Electrostatic MEMS Research Articles

Electrostatic MEMS Two-Dimensional Scanning Micromirrors Integrated with Piezoresistive Sensors

The MEMS scanning micromirror requires angle sensors to provide real-time angle feedback during operation, ensuring a stable and accurate deflection of the micromirror. This paper proposes a method for integrating piezoresistive sensors on the torsion axis of electrostatic MEMS micromirrors to detect the deflection angle. The design uses a multi-layer bonding process to realize a vertical comb-driven structure. The device structure is designed as a double-layer structure, in which the top layer is the ground layer and integrates with piezoresistive sensor. This approach avoids crosstalk between the applied drive voltage and the piezoresistive sensor. This design also optimizes the sensor’s size, improving sensitivity. A MEMS two-dimensional (2D) scanning micromirror with a 1 mm mirror diameter was designed and fabricated. The test results indicated that, in a vacuum environment, the torsional resonance frequencies of the micromirror’s fast axis and slow axis were 17.68 kHz and 2.225 kHz, respectively. When driving voltages of 33 V and 40 V were applied to the fast axis and slow axis of the micromirror, the corresponding optical scanning angles were 55° and 45°, respectively. The piezoresistive sensor effectively detects the micromirror’s deflection state, and optimizing the sensor’s size achieved a sensitivity of 13.87 mV/V/°. The output voltage of the piezoresistive sensor shows a good linear relationship with the micromirror’s deflection angle, enabling closed-loop feedback control of the electrostatic MEMS micromirror.

Exploiting Nonlinearities of Electrostatic MEMS Resonators for Tunable Low Pressure Sensing

In this paper, we demonstrate the potential functionalization of inherent nonlinearities associated with electrostatic MEMS resonators for low air pressure applications, with operating ranges as low as 0.65-295 mbar. The proposed pressure sensor is made of a polysilicon microplate subject to electrostatic actuation via an underneath electrode and attached to two cantilever microbeams. The pressure sensing mechanism relies on the motion-induced current method, a transduction mechanism that converts the dynamic alteration of the microplate due to pressure variations into an electrical signal detected via a lock-in amplifier. The experimental study showed evidence of the possible tunability of the pressure sensor via the deployment of different detection mechanisms to achieve superior performance in terms of sensitivity and low pressure operating range. These mechanisms rely on nonlinear dynamic features that result from the strong coupling between the microplate and the surrounding fluid along with the electrostatic actuation. These include dynamic pull-in instability, bifurcation and softening behavior associated with the elastic effect of the squeeze-film damping. The experimental results revealed that tracking the bifurcation frequency allows for the detection of low pressure levels, in the range of a few millibars. This capability is not provided by the resonance frequency shift method, which, while offering higher sensitivity, does not achieve the same low-pressure detection.

Flexural–torsional modal interaction in MEMS actuators initiated by minuscule asymmetry

AbstractAn efficient actuation technique for electrostatic MEMS actuators exploiting electro-mechanical-mechanical modal interactions is proposed. The flexural–torsional equations of motion are established, and we manifest that the initiation of a 2:1 autoparametric modal interaction between in-plane bending and torsional modes of the actuator that is supposed to be symmetrical with respect to its axis of rotation is contingent upon the presence of a quadratic stiffness term, which arises from the existence of non-zero first moments of area of the actual cross-section in prismatic microbeams. In order to efficiently reduce the AC voltage value required to reach the activation of the 2:1 mechanical modal interaction, the electrical resonant frequency is syntonized to half of the natural frequency of the in-plane bending mode. The results indicate that the amplitude of the in-plane motion saturates upon the initiation of an energy exchange between the bending and torsional motions. Through suitable tuning of the AC frequency, the amplitude of the in-plane motion is minimized, while the amplitude of the torsional motion, the indirectly excited mode, is maximized. Our results demonstrate that the actuator's torsional motion, when subjected to a 1:2:1 electro-flexural–torsional modal interactions, is triggered by applying a maximum voltage of 10 V, resulting in about 20 degrees rotational angle. Furthermore, prolific frequency combs are generated as a result of secondary Hopf bifurcations along the large-amplitude response branches, inducing quasi-periodicity in the MEMS dynamics.

Differential capacitive mass sensing based on mode localization in coupled microbeam arrays

In this paper, we developed a multi-physics model of an electrostatic MEMS resonator made of an array of mechanically-coupled beams and investigate its potential use for mass detection applications. Experiments were conducted on two- and three-coupled beams under electrostatic actuation to verify the capability of the model to predict the mechanical response of coupled beam arrays. The fabricated device, comprising polysilicon-coupled microbeams, is produced using the Multi-User MEMS Processes, followed by an experimental investigation. Numerical results were found in good agreement with their experimental counterparts. The developed model was used to demonstrate the possible adjustment of the electrostatic actuation to enhance the sensitivity of the dynamic response of the coupled MEMS resonator to mass perturbations. By leveraging the mode localization phenomenon and incorporating a novel differential capacitance sensing mechanism, a notable 84% improvement in sensitivity when switching from two-beam to three-beam system while operating near the second mode in the linear regime. Actuating the MEMS device at higher voltages enabled to achieve higher sensitivity thanks to the activation of nonlinear effects such as bifurcation and softening. We observed the transition from nonlinear to nearly-linear dynamic response of the coupled beams upon the addition of mass and demonstrated how bifurcations that cause a sudden shift to a high-amplitude motion can be utilized in differential capacitance-based mass sensing. Additionally, the suggested detection mechanism allows for overcoming the inherent parasitic capacitance, thereby mitigating low signal-to-noise ratios.

Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

PurposeBased on previous results of the existence, uniqueness, and regularity conditions for a continuous dynamic model for a parallel-plate electrostatic micro-electron-mechanical-systems with the fringing field, the purpose of this paper concerns a Galerkin-FEM procedure for deformable element deflection recovery. The deflection profiles are reconstructed by assigning the dielectric properties of the moving element. Furthermore, the device’s use conditions and the deformable element’s mechanical stresses are presented and discussed.Design/methodology/approachThe Galerkin-FEM approach is based on weighted residuals, where the integrals appearing in the solution equation have been solved using the Crank–Nicolson algorithm.FindingsBased on the connection between the fringing field and the electrostatic force, the proposed approach reconstructs the deflection of the deformable element, satisfying the conditions of existence, uniqueness and regularity. The influence of the electromechanical properties of the deformable plate on the method has also been considered and evaluated.Research limitations/implicationsThe developed analytical model focused on a rectangular geometry.Practical implicationsThe device studied is suitable for industrial and biomedical applications.Originality/valueThis paper proposed numerical approach characterized by low CPU time enables the creation of virtual prototypes that can be analyzed with significant cost reduction and increased productivity.

Unraveling the nature of sensing in electrostatic MEMS gas sensors

This paper investigates the fundamental sensing mechanism of electrostatic MEMS gas sensors. It compares among the responsivities of a set of MEMS isopropanol sensors before and after functionalization, and in the presence and absence of electrostatic fields when operated in static and dynamic detection modes. In the static mode, we found that the sensors do not exhibit a measurable change in displacement due to added mass. On the other hand, bare sensors showed a clear change in displacement in response to isopropanol vapor. In the dynamic mode, functionalized sensors showed a measurable frequency shift due to the added mass of isopropanol vapor. In the presence of strong electrostatic fields, the measured frequency shift was found to be threefold larger than that in their absence in response to the same concentration of isopropanol vapor. The enhanced responsivity of dynamic detection allows the sensors to measure the vapor mass captured by the functional material, which is not the case for static detection. The detection of isopropanol by bare sensors in static mode shows that change in the medium permittivity is the primary sensing mechanism. The enhanced responsivity of dynamic mode sensors when operated in strong electrostatic fields shows that their sensing mechanism is a combination of a weaker added mass effect and a stronger permittivity effect. These findings show that electrostatic MEMS gas sensors are independent of the direction of the gravitational field and are, thus, robust to changes in alignment. It is erroneous to refer to them as ‘gravimetric’ sensors.

Biomechanical MEMS Electrostatic Energy Harvester for Pacemaker Application: A Study of Optimal Interface Circuit.

The leadless pacemaker is the most recent pacemaker concept, developed to overcome conventional pacemakers' limitations. This technology offers better comfort to the patients, lower risk from implantation, and higher reliability. However, these devices suffer from limited battery lifetime due to the extreme miniaturization required for implantation inside the heart cavities. This work proposes extending the battery lifetime by converting biomechanical heartbeat energy into electricity using an innovative electrostatic MEMS energy harvesting device. Based on theoretical models and experiments, we propose a general approach to choosing the optimal interface circuit which considers the parasitic capacitance of the circuit, as it is an imperfection that significantly affects the power performance. According to the energy consumed by the last generation commercial leadless pacemakers, the proposed MEMS solution with optimal interface circuit experimentally showed the possibility of extending the pacemaker battery lifetime by up to 44%.

Development of MEMS gas sensors equipped with metal organic frameworks

In this study, we investigate the potential usage of electrostatic MEMS resonators for CO2 sensing. The MEMS sensor consists of two cantilever microbeams supporting a microplate coated with a Metal Organic Framework (MOF), namely ZIF-8. The detector material, ZIF-8, is synthesized using eco-friendly and sustainable production techniques and then deposited on the microplate to functionalize the sensor. An experimental setup, deploying the motion-induced current technique, is implemented and deployed to analyze the response of the gas sensor upon exposure to CO2. This method relies on a conversion mechanism that detects the motion of the sensor and translates it into a current signal. The experiments demonstrated the capability of the developed gas sensor to detect CO2. Motion-induced current measurements detected the nonlinear dynamic features of the sensor resulting from the presence of CO2 in various concentrations. We show effective deployment of frequency and amplitude changes in peak output current as detectors for the presence of CO2 and quantifiers of its concentration. Following the frequency-based approach, the sensor achieved a sensitivity of S=0.105 Hz/ppm. We also investigated a CO2 sensing mechanism that relies on the sudden and significant increase in the current amplitude at the onset of bifurcation. This sensing mechanism reached a sensitivity of S=0.903 pA/ppm.

Bidirectional electrostatic MEMS-tunable VCSELs.

Microelectromechanical system (MEMS) vertical cavity surface-emitting lasers (VCSELs) are the fastest coherently tunable lasers (nm/ns) due to their unique Doppler-assisted tuning mechanism. However, in standard electrostatic actuation, the response is highly nonlinear and large (>100 V) dynamic voltages are needed for MHz sweep rates. We present a bidirectional MEMS VCSEL as a solution to these challenges where static voltages can be used to enable substantially linear and amplified wavelength tuning with respect to the fast tuning (MEMS) voltage. Using an InP/SOI MEMS bonded structure, we show a tuning range of 54.5 nm (gain limited) centered around 1586 nm at an actuation frequency of 2.73 MHz.

Equivalent Circuit Modeling of Air-Coupled Laterally Actuated Electrostatic Bulk-Mode MEMS

Equivalent Circuit Modeling of Air-Coupled Laterally Actuated Electrostatic Bulk-Mode MEMS

Electrostatic MEMS Speakers With Embedded Vertical Actuation

Electrostatic MEMS Speakers With Embedded Vertical Actuation

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.

Dynamic analysis of a novel two-sided nonlinear MEMS electrostatic energy harvester

In this work, we investigate the frequency response of an electrostatic MEMS energy harvester with innovative gap-overlap transducer design. We prove theoretically and experimentally that this design solution gives rise to a strongly nonlinear behaviour in MEMS dynamics. This is the first time that this phenomenon is demonstrated in a gap-overlap electrostatic MEMS along with a theoretical explanation. When increasing the bias voltage, the frequency response shifts towards lower frequencies while bending towards higher ones. The main consequence of this bending is a significant increase of the system bandwidth (+280 % compared to a linear situation with no bias voltage for the same device) when the bias voltage increases up to 30 V. A proposed gap-overlap transducer configuration is demonstrated to be a simple and efficient solution for MEMS energy harvester bandwidth increase.

Tracking of bifurcations and hysteresis in electrostatically actuated resonators by motion-induced current

In this work, we present an experimental technique to detect the onset of bifurcation and measure the extent of hysteresis in electrostatic MEMS. The device-under-test comprises a microcantilever beam actuated via a side electrode. The beam vibrations result in varying the resonator’s capacitance, therefore inducing a current that can be measured and used for characterization and performance analysis. The motion-induced current is measured, and its harmonics are extracted using a lock-in amplifier. Locking on the third harmonic of the induced current enables us to bypass parasitic capacitance and extract a signal directly related to the resonator motions. We show that this signal can be used to investigate the nonlinear dynamic behavior of MEMS resonators undergoing large motions. Specifically, our experiments demonstrate our technique's ability to detect various bifurcations, to track the onset of hysteresis, and to measure the hysteresis bandwidth. We also use our technique to analyze the quantitative relationships between the actuation voltage, the location of the bifurcation point, and the hysteretic bandwidth. Finally, we show that our technique can be used to generate the calibration curves for inertial MEMS sensors.

Super-twisting Sliding Mode Control Based on Electrostatic MEMS Micromirror Scanning

In this paper, a Super-twisting sliding-mode control method based on a nonlinear interference observer is proposed for the external perturbation of MEMS micromirrors during beam scanning. Developing a physical model of electrostatic MEMS micromirror, the Super-twisting sliding-mode control algorithm based on nonlinear interference observer is applied to the electrostatically driven MEMS scanning micromirror with side electrodes, with the demonstration on stability of the control system by Lyapunov theory. The method effectively improves the anti-disturbance performance of the system. The simulation results show that the Super-twisting sliding mode control method based on nonlinear disturbance observer can effectively enhance the disturbance inhibition of the system.

High-reliability circular-contact RF MEMS switches in silicon hermetic package

This paper presents a highly reliable direct-contact electrostatic RF MEMS switch. To enhance the reliability, the contact structure of the switch is designed into a circular shape, and the bottom contact surface is covered by a hard metal Pt layer. In addition, a high resistance silicon cap is used for hermetic packaging of the switch structure. By theoretical calculation and FEM simulation, parameters of the switch structure as well as its packaging are co-designed and optimized. During fabrication, the circular contact structure is formed by a three-step etching process; and after fabrication, the silicon hermetic packaging is realized by epoxy bonding and multi-step dicing process. The measured insertion loss and isolation of the switch with package is −0.41@20 GHz, and −20.9@20 GHz. Due to the optimized design, the RF performance of the switch remains almost unchanged before and after packaging. The measured driving voltage is 50–60 V, and the ON/OFF switching time is 25 μs/5 μs. The lifetime test shows that the switch passes the 2.6 billion times hot switching at the working power of 25 dBm. Finally, the switch also shows good performances in package leak rate test.

Self-excited MEMS Oscillator using an Electrostatic Cantilever

In this paper, we propose a new use of an electrostatic MEMS cantilever structure as a voltage-controlled oscillator (VCO). A cantilever made of plated gold is accompanied with a drive electrode to turn on the contact switch upon voltage application. The electrical interconnection is arranged to discharge the cantilever when it is brought into contact with the switch, thereby promptly losing the electrostatic force and opening the contact switch again. As a result, the electrostatic cantilever spontaneously repeats the electrostatic pull-in and release at a frequency determined by the DC level of the applied voltage. A metallic cantilever of 500 μm long, 8 μm wide, and 12 μm thick is experimentally confirmed to work as an VCO in the frequency range between 8.4 kHz and 10.7 kHz controlled by the DC voltage between 160V and 180V.

Study on sinusoidal estimation deviation of electrostatic actuated MEMS mirror torsion angle

Electrostatic MEMS micromirrors usually work in resonant state to obtain large amplitude of torsion angle. The real-time prediction of MEMS micromirror torsion angle is calculated according to the measured resonant amplitude and phase under the assumption that the relationship between the torsion angle and time is sinusoidal. However, there are few reports on the deviation of this torsion angle predication based on sinusoidal assumption. In this paper, the real resonant torsion trajectory of C1100 MEMS micromirror under different driving frequencies and voltages is measured by using microscopic laser Doppler method, and the deviation between the real trajectory and the trajectory fitted by sinusoidal curve is compared. The results show that the real trajectory of the MEMS micromirror driven by square wave is not completely consistent with the sinusoidal estimation, and the deviation increases with the increase of the torsional angle amplitude. By obtaining the frequency domain components of the torsion angle signal using FFT method, the main reason of this prediction deviation is due to composition of harmonic signals on base frequency signal. The research results reveal that the sinusoidal assumption method is only suitable for situations when the optical angle accuracy is less than 0.1°.

Boosting the Electrostatic MEMS Converter Output Power by Applying Three Effective Performance-Enhancing Techniques.

This current study aims to enhance the electrostatic MEMS converter performance mainly by boosting its output power. Three different techniques are applied to accomplish such performance enhancement. Firstly, the power is boosted by scaling up the technology of the converter CMOS accompanied circuit, the power conditioning, and power controlling circuits, from 0.35 µm to 0.6 µm CMOS technology. As the converter area is in the range of mm2, there are no restrictions concerning the scaling up of the accompanied converter CMOS circuits. As a result, the maximum voltage of the system for harvesting energy, Vmax, which is the most effective system constraint that greatly affects the converter's output power, increases from 8 V to 30 V. The output power of the designed and simulated converter based on the 0.6 µm technology increases from 2.1 mW to 4.5 mW. Secondly, the converter power increases by optimizing its technological parameters, the converter thickness and the converter finger width and length. Such optimization causes the converter output power to increase from 4.5 mW to 11.2 mW. Finally, the converter structure is optimized to maximize its finger length by using its wasted shuttle mass area which does not contribute to its capacitances and output power. The proposed structure increases the converter output power from 11.2 mW to 14.29 mW. Thus, the three applied performance enhancement techniques boosted the converter output power by 12.19 mW, which is a considerable enhancement in the converter performance. All simulations are carried out using COMSOL Multiphysics 5.4.

Solution Properties of a New Dynamic Model for MEMS with Parallel Plates in the Presence of Fringing Field

In this paper, starting from a well-known nonlinear hyperbolic integro-differential model of the fourth order describing the dynamic behavior of an electrostatic MEMS with a parallel plate, the authors propose an upgrade of it by formulating an additive term due to the effects produced by the fringing field and satisfying the Pelesko–Driscoll theory, which, as is well known, has strong experimental confirmation. Exploiting the theory of hyperbolic equations in Hilbert spaces, and also utilizing Campanato’s Near Operator Theory (and subsequent applications), results of existence and regularity of the solution are proved and discussed particularly usefully in anticipation of the development of numerical approaches for recovering the profile of the deformable plate for a wide range of applications.