Pull-in State Research Articles

Design, Modeling, and Optimization of a Bistable Electromagnetic Actuator With Large Deflection

This letter presents the design, modeling, and optimization of a bistable electromagnetic actuator of size 2.2 mm × 2.2 mm, consisting of a hard magnet membrane, a planar coil, and a permanent magnet. An analytical model is established to calculate the magnetic field generated by the coil, which is validated by the finite-element method. Based on the theoretical analysis of magnetic force, the actuator's parameters are optimized to maximize the magnetic force for large deflection. Moreover, a multiphysics simulation is implemented to characterize the electromagnetic and mechanical performance to predict the static response. We developed an actuator with process feasibility and a deflection of 140 μm, which can maintain the pull-in state without power consumption. The simulation and analytical results are in good agreement, demonstrating the accuracy and practicality of the methodology for a wide spectrum of electromagnetic actuators.

Comparison of Si3N4-SiO2 and SiO2 Insulation Layer for Zero-Bias CMUT Operation Using Dielectric Charging Effects.

In this letter, we report the characteristics of zero-bias capacitive micromachined ultrasonic transducers (CMUTs) in various aspects, considering the transmission and reception sensitivity and evaluation of the long-term stability with ac transmission in immersion. The main idea of the zero-bias CMUT implementation is that the charge is injected by the dielectric charging effects in an insulation layer in the pull-in state. The CMUT was fabricated by a local oxidation of silicon (LOCOS) process, and the insulation layer consists of Si3 N4 -SiO2 and SiO2, which have been commonly used in previous studies. A study on the charging effects is reported to quantitatively observe the voltage shift by charge transfer with time dependence at different temperatures and collapsing time dependence. Therefore, we successfully implemented a zero-bias CMUT with a transmission efficiency of 4.62 kPa/V at a center frequency of 7.53 MHz in Si3 N4-SiO2 and a transmission efficiency of 6.78 kPa/V at a center frequency of 7.86 MHz in SiO2 immersion.

Charging mechanisms in Y2O3 dielectric films for MEMS capacitive switches

The potential application of Yttrium Oxide (Y2O3) in capacitive Micro-Electro-Mechanical Switches (MEMS) dielectric films is investigated. The electrical properties and the impact of electrical stress on capacitive switches have been investigated with the aid of Metal-Insulator-Metal (MIM) capacitors and MEMS capacitive switches in order to determine the suitability of this material for such application. The assessment in MIMs consisted of recording the current-voltage characteristics in order to determine the transport mechanisms and the charge injection by injecting electrodes during the charging process. The MEMS switches were employed to monitor the charge injection through the bridge during pull-in state and collection during the pull-up state. The process was performed under different stress conditions in order to determine the impact of stressing electric field intensity.

Comprehensive numerical modeling of the nonlinear structural behavior of MEMS/NEMS electrostatic actuators under the effect of the van der Waals forces

The mechanical behavior of MEMS/NEMS based-actuators has been studied in this work while considering the effect of both electrostatic and van der Waals forces. The assumed structural model was constructed based on an Euler–Bernoulli beam continuous nonlinear model, where both the mid-plane stretching (geometric nonlinearity) and the electric fringing-fields effects have been taken into consideration. The nonlinear equation of motion of the actuator governing its static behavior has been derived. An original Galerkin expansion based reduced-order model has been developed to avoid problem arising from all the possible nonlinearities in the nonlinear differential equation. The obtained reduced-order model equations have been resolved mathematically using the so-called Newton-Raphson technique. The developed numerical method was shown to be powerful in examining the basic pull-in design parameters such as the electric load amplitude and the beam static deflection at the pull-in instability state. The model also proved its capability in capturing the effect of the actuator parameter on its detachment length due to the attractive van der Waals forces. Some of the obtained numerical outcomes have been compared with other numerical approaches such as finite-elements and finite-difference methods. The assessment revealed acceptable agreement among all assumed numerical techniques.

Thermal and surface effects on the pull-in characteristics of circular nanoplate NEMS actuator based on nonlocal elasticity theory

This paper aims to investigate the coupling influences of thermal loading and surface effects on pull-in instability of electrically actuated circular nanoplate based on Eringen's nonlocal elasticity theory, where the electrostatic force and thermally corrected Casimir force are considered. By utilizing the Kirchhoff plate theory, the nonlinear equilibrium equation of axisymmetric circular nanoplate with variable coefficients and clamped boundary conditions is derived and analytically solved. The results describe the influences of surface effect and thermal loading on pull-in displacements and pull-in voltages of nanoplate under thermal corrected Casimir force. It is seen that the surface effect becomes significant at the pull-in state with the decrease of nanoplate thicknesses, and the residual surface tension exerts a greater influence on the pull-in behavior compared to the surface elastic modulus. In addition, it is found that temperature change plays a great role in the pull-in phenomenon; when the temperature change grows, the circular nanoplate without applied voltage is also led to collapse.

A coupled bending-torsion model for electrostatically actuated torsional nano/micro-actuators with considering influence of van der Waals force

In the current paper, a coupled two degree of freedom model which considers both bending and torsion of the supporting torsion beams is presented for electrostatically actuated torsional nano/micro-actuators under the effect of van der Waals (vdW) force. Newton’s second law is utilized for finding the normalized equations governing the static behavior of the actuator. The implict function theorem is then utilized for finding the equations governing the pull-in state of the actuator. The related results show that torsion model considerably overestimates the pull-in parameters of the nano/micro-actuator. The concept of the instability mode is introduced, and it is shown that when the ratio of the bending stiffness to the torsion stiffness of the supporting torsion beams is relatively low, the dominant instability mode of the actuator would be the bending mode and otherwise the dominant instability mode would be the torsion mode. It is also observed that the presence of the vdW force can significantly reduce the pull-in angle and pull-in deflection of the nano/micro-actuator. The presented results also show that the vdW force can lead to considerable reduction in the pull-in voltage of the actuator. The equilibrium behavior of the actuator is studied, and it is observed that the vdW force and also bending of the supporting torsion beams greatly reduce the maximum allowable voltage which can be applied to the actuator. Results of this paper can be used for successful design of electrostatically actuated torsional nano/micro-actuators where the size of the actuator is sufficiently small, and as a result, the vdW force plays a major role in the system.

Characterization of the static behavior of micromirrors under the effect of capillary force, an analytical approach

In this article, the static behavior of micromirrors under the effect of capillary force is studied. The dimensionless equations governing the static behavior and the pull-in state of the micromirror under capillary force are obtained, and the effects of different geometrical parameters on the pull-in angle of micromirrors are investigated. The static behavior of micromirrors is studied both numerically and analytically using the homotopy perturbation method. It is observed that with increasing the instability number defined in this article, the rotation angle of the micromirror is increased and suddenly the pull-in occurs. The results of the presented model are then verified by comparing them with the results of finite element simulations performed in the commercial finite element model software ANSYS. The agreement between the results of finite element model and those of the proposed analytical model shows that homotopy perturbation method can be used as a fast and accurate tool for predicting mirror’s behavior under capillary force.

Design and simulation of a carbon nanotube-based adjustable nano-electromechanical shock switch

In this paper, design and simulation of a carbon nanotube-based nano-electromechanical shock switch is reported. The switch is represented by a carbon nanotube placed over a ground electrode. Response of the nano-switch based on nonlinear beam theory is studied using Galerkin’s method. Up to five mode shapes have been utilized to capture the response of system and results are validated by comparing with Molecular Dynamics (MD) simulation. Due to their high stiffness, CNTs cannot be actuated to pull-in (switch ON) state by conventional mechanical shocks in range of 10–1000g under one-step voltage. Here, a multi-steps voltage modification is applied to enhance the actuation. Employing this method, a nano-switch with fixed geometry can be adjusted to be triggered by wide rang of mechanical shocks (10–1000g).

Floating electrode microelectromechanical system capacitive switches: A different actuation mechanism

The paper investigates the actuation mechanism in floating electrode microelectromechanical system capacitive switches. It is demonstrated that in the pull-in state, the device operation turns from voltage to current controlled actuation. The current arises from Poole-Frenkel mechanism in the dielectric film and Fowler-Nordheim in the bridge-floating electrode air gap. The pull-out voltage seems to arise from the abrupt decrease of Fowler-Nordheim electric field intensity. This mechanism seems to be responsible for the very small difference with respect to the pull-in voltage.

Design, fabrication and characterization of a high fill-factor micromirror array for wavelength selective switch applications

This paper presents the design, fabrication and characterization of a high fill-factor micromirror array in application of wavelength selective switch (WSS). The micromirror array consists of 52 independent micromirrors. Each micromirror is composed of a cantilever-type micromirror plate (800 μm × 120 μm) with a bumper and an eight-terraced bottom electrode with a limiting plane. A cantilever beam is designed to obtain the rotation angle of micromirror plate and achieve a high fill-factor for the micromirror array. Meanwhile, the bumper and limiting plane are used to prevent the damage possibly caused by the pull-in effect or some vibration instance. An eight-terraced electrode is utilized for reducing the driving voltage. The micromirror array with a high fill-factor in excess of 97% has been successfully achieved using the bulk micromachining technologies. The measured static and dynamic characteristics show that the micromirror can achieve a maximal rotation angle of 0.87° with a Direct Current (DC) driving voltage of 156 V. The turn-on responding time is 0.57 ms, and the turn-off responding time is 4.36 ms. Furthermore micromirror plate can be easily released from the pull-in state without damaged due to the novel bumper design. The switching function between the two output ports of a WSS optical system has also been demonstrated.

Analysis for Pull-In Voltage of a Multilayered Micro-Bridge Driven by Electrostatic Force

A trial solution for bending deflection of a multilayered micro-bridge subject to a voltage induced load is presented. The relation between the applied voltage and the displacements of the micro-bridge in the pull-in state is analyzed by energy method. Furthermore, two analytical expressions about normalized displacement and pull-in voltage are carried out. It’s proved that the value of normalized displacement is not influenced by residual stress if axial and shear deformation is ignored. Finally, the theoretical results are compared with that of FEM, and they show good agreement.

Microbeam pull-in voltage topology optimization including material deposition constraint

Because of the strong coupling between mechanical and electrical phenomena existing in electromechanical microdevices, some of them experience, above a given driving voltage, an unstable behavior called pull-in effect. The present paper investigates the application of topology optimization to electromechanical microdevices for the purpose of delaying this unstable behavior by maximizing their pull-in voltage. Within the framework of this preliminary study, the pull-in voltage maximization procedure is developed on the basis of electromechanical microbeams reinforcement topology design problem. The proposed sensitivity analysis requires only the knowledge of the microdevice pull-in state and of the first eigenmode of the tangent stiffness matrix. As the pull-in point research is a highly non-linear problem, the analysis is based on a monolithic finite element formulation combined with a normal flow algorithm (homotopy method). An application of the developed method is proposed and the result is compared to the one obtained using a linear compliance optimization. Moreover, as the results provided by the developed method do not comply with manufacturing constraints, a deposition process constraint is added to the optimization problem and its effect on the final design is also tested.

An efficient DIPIE algorithm for CAD of electrostatically actuated MEMS devices

Pull-in parameters are important properties of electrostatic actuators. Efficient and accurate analysis tools that can capture these parameters for different design geometries, are therefore essential. Current simulation tools approach the pull-in state by iteratively adjusting the voltage applied across the actuator electrodes. The convergence rate of this scheme gradually deteriorates as the pull-in state is approached. Moreover, the convergence is inconsistent and requires many mesh and accuracy refinements to assure reliable predictions. As a result, the design procedure of electrostatically actuated MEMS devices can be time-consuming. In this paper a novel Displacement Iteration Pull-In Extraction (DIPIE) scheme is presented. The DIPIE scheme is shown to converge consistently and far more rapidly than the Voltage Iterations (VI) scheme (>100 times faster!). The DIPIE scheme requires separate mechanical and electrostatic field solvers. Therefore, it can be easily implemented in existing MOEMS CAD packages. Moreover, using the DIPIE scheme, the pull-in parameters extraction can be performed in a fully automated mode, and no user input for search bounds is required.