Bistable Microelectromechanical System Research Articles

Ising Machine Based on Bistable Microelectromechanical Systems

We propose an Ising machine made of microelectromechanical systems (MEMS), where the annealing process is automatically executed by a dissipation mechanism. The core structure is a series of buckled plates. Two stable positions of each plate (left and right) represent its binary state acting as a bit so that a plate works as a mechanical memory. The electrostatic interaction between adjacent plates is introduced by applying voltage. Plates continue to flip between two stable buckled positions until the series of plates reaches a local minimum due to the damping of the mechanical motion. \red{First, we design Ising machines simulating a ferromagnetic (FM) interaction and an antiferromagnetic (AF) interaction separately. Then, we propose a fully-connected MEMS\ network representing a coexistence system of FM and AF interactions in an arbitrary way, by way of which an arbitrary combinatorial problem described by the Ising model can be solved.} The present mechanism works at room temperature without external magnetic field, which is very different from the standard classical or quantum annealing mechanism.

Reducing Dynamism in DRAM With Bistable MEMS Switch as Sleep Transistor

We demonstrate the bistable microelectromechanical system (MEMS) sleep-transistor for CMOS integrated circuits (ICs). The sleep transistor has infinite sleep mode resistance and ~2.5-Ω resistance in active mode. The hold bias in active mode is zero for the bistable MEMS sleep transistor. The proposed bistable MEMS switch is an ideal candidate for gating the power-hungry digital circuits. The dynamic random access memory (DRAM) supply rails gated with bistable MEMS sleep transistors offer ~6 order reduction in refresh rate. This article also reports on the design guidelines for the CMOS compatible fabrication of bistable MEMS sleep transistor. Only ~0.31 pJ of energy is consumed, in toggling between the modes of bistable MEMS sleep transistor. The MEMS gate can drive large area CMOS circuit blocks with fuse current density of ~0.5 mA/μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Furthermore, the fabrication of the bistable MEMS sleep transistor is critical in the aspect that its design is a play between restoring and adhesion forces.

Switching performance of bistable membranes activated with integrated piezoelectric thin film transducers

In this paper we report on the fabrication of bistable micro electromechanical systems (MEMS) membranes, which have diameters in the range of 600–800 µm, a total thickness of 3.13 µm and feature integrated low power piezoelectric transducers based on aluminium nitride. To estimate the impact of the membrane asymmetry due to the integrated piezoelectric transducers, an asymmetric constant in the potential energy calculation of the bistable system is introduced, thus enabling a proper theoretical prediction of the membrane behaviour. To switch between the two bistable ground states, rectangular pulses with frequencies in the range of 50–100 kHz and a peak-to-peak voltage of 30 Vpp are applied. Two different actuation schemes were investigated, whereas one shows positive and the other negative pulse amplitudes. With a Laser-Doppler Vibrometer the velocity of the membranes during the bistable switching process is measured and integrated over time to calculate the membrane displacement in the centre. FFT (fast Fourier transform) spectra of an applied broadband white noise signal were determined in both ground states and showed a strongly decreased dominant resonance frequency in the lower ground state. The results also showed, that the asymmetry of the system causes different switching behaviours for each bistable ground state, whereas it requires less energy to switch from the lower to the upper ground state. Furthermore, it was demonstrated that a minimum of two pulses are needed for switching when using positive rectangular pulses of 30 Vpp in contrast to four when applying negative pulses. The pulse frequency causing switching was in the range of 60–110 kHz, strongly depending on the geometry and applied signal scheme. Additionally, a positive voltage offset applied to the pulse signal characteristics resulted in both a wider range of frequencies suitable for switching and in a decrease of the dominant resonance frequency, which is also beneficial for the switching process and indicates the potential for efficient switching of bistable MEMS membranes.

Size-dependent nonlinear behavior of a piezoelectrically actuated capacitive bistable microstructure

Size-dependent behavior of a bistable microelectromechanical system subjected to electrostatic and piezoelectric actuations is investigated. The system is comprised of an Euler–Bernoulli slightly curved capacitive microbeam which is laminated between piezoelectric layers. Applying DC voltage to piezoelectric layers induces axial force in the beam and modulates its stiffness and consequently, its frequencies. Hamilton’s principle is used to derive the governing equation of motion and the size effect is introduced into the formulation through the so-called strain gradient theory. The proposed model accounts for nonlinearities due to mid-plane stretching, curvature, and the electrostatic loading. The reduced order model is obtained via utilizing the Galerkin approach. A detailed study is carried out to reveal the influences of initial curvature, size effect, and piezoelectric actuation on the behavior of the system. The primary resonance is characterized using shooting method and the stability of the limit cycles is determined using the Floquet theorem. The results are compared in some cases with the method of multiple time scales. The static and dynamic snap-through are identified and the influences of the system parameters on the snap-through bandwidth is investigated. It is shown that by applying appropriate piezoelectric actuation, the bandwidth and center frequency of the dynamic snap-through as well as the static bistability band can be tuned effectively. The results can be used in design and analysis of bistable MEMS-based devices especially in switch and filter design applications.

Frontispiece: A Bistable Microelectromechanical System Actuated by Spin‐Crossover Molecules

Frontispiece: A Bistable Microelectromechanical System Actuated by Spin‐Crossover Molecules

A Bistable Microelectromechanical System Actuated by Spin‐Crossover Molecules

AbstractWe report on a bistable MEMS device actuated by spin‐crossover molecules. The device consists of a freestanding silicon microcantilever with an integrated piezoresistive detection system, which was coated with a 140 nm thick film of the [Fe(HB(tz)3)2] (tz=1,2,4‐triazol‐1‐yl) molecular spin‐crossover complex. Switching from the low‐spin to the high‐spin state of the ferrous ions at 338 K led to a reversible upward bending of the cantilever in agreement with the change in the lattice parameters of the complex. The strong mechanical coupling was also evidenced by the decrease of approximately 66 Hz in the resonance frequency in the high‐spin state as well as by the drop in the quality factor around the spin transition.

A Bistable Microelectromechanical System Actuated by Spin-Crossover Molecules.

We report on a bistable MEMS device actuated by spin-crossover molecules. The device consists of a freestanding silicon microcantilever with an integrated piezoresistive detection system, which was coated with a 140 nm thick film of the [Fe(HB(tz)3 )2 ] (tz=1,2,4-triazol-1-yl) molecular spin-crossover complex. Switching from the low-spin to the high-spin state of the ferrous ions at 338 K led to a reversible upward bending of the cantilever in agreement with the change in the lattice parameters of the complex. The strong mechanical coupling was also evidenced by the decrease of approximately 66 Hz in the resonance frequency in the high-spin state as well as by the drop in the quality factor around the spin transition.

Fabrication and investigation of low actuation voltage curved beam bistable MEMS switch

Fabrication and characterization of a novel bistable MEMS (MicroElectroMechanical Systems)-based switch is reported in this paper. The bistable switch is fabricated on SOI wafer with 10 µm thick device Si layer using Silicon-On-Insulator Multi User MEMS Process with three masks. The proposed device is comprised of a centrally clamped parallel curved beams (switching element) and a pair of electrothermal V-beam microactuators (actuating element). The bistability is achieved through the buckling of centrally clamped parallel curved beams and the critical buckling load is provided by the electro-thermal expansion of the V-beam microactuators. Hinges, latches, membranes are not used in the proposed design and thus the fabrication complexity is reduced to a greater extent. A maximum displacement of 20.7 µm is achieved at 14 V DC supply for the V-beam microactuator and this thermal expansion of the V-beam microactuator acted as the critical buckling load for the centrally clamped parallel curved beam. Electrical and mechanical characterization of switch is performed and after the analysis, it is verified that the nonlinear property (elasticity) of silicon material is poor and that is the reason for comparatively higher actuation voltage to simulation results. A novel optimized redesign for the electrothermal V-beam microactuator based on POLYMUMPs process is proposed in order to overcome the uncertainties endured.

Feasibility of energy harvesting from a rotating tire based on the theory of stochastic resonance

Recently the use of nonlinear bi-stable micro-electro mechanical systems (MEMS) to achieve automobile tire vibration power generation has made some progress. However, the theory of stochastic resonance has not been successfully applied to automobile tires, which can produce a larger vibrational response than for a typical resonance while inputting a weak periodic force and noise excitation into a nonlinear bi-stable system. Hence, in this paper, in view of the principle of stochastic resonance, a new model is derived by positioning a magnetic end mass attached to a cantilever beam and another permanent magnet with the same polarity on the frame. Due to the road noise excitation along with the periodic force inputted to the mechanism, whether the phenomenon of stochastic resonance can happen will be discussed. Meanwhile, on the basis of Kramers rate and duffing equations the preliminary experimental device is also designed.

Investigation on Mechanically Bistable MEMS Devices for Energy Harvesting From Vibrations

In this paper, mechanically bistable microelectromechanical systems devices are investigated for energy harvesting from mechanical vibrations. This approach is particularly suitable when random, weak, and broad-band vibrations in the low-frequency range are considered. These working conditions are, in fact, quite challenging and are often approached via arrays of linear resonant microdevices. Our approach allows, with a single device, to efficiently collect kinetic energy in the whole spectrum of frequencies of the incoming signal. Bistable behaviors are achieved through purely mechanical and fully compliant micromechanisms. Different structures have been analytically and numerically investigated, both in static and dynamic working conditions, and optimized results are proposed. The advantages of the proposed device, which exploit bistable dynamic behaviors, over linear and monostable strategies are presented in this paper: In the case of the incoming kinetic energy spread over a large bandwidth and confined at low frequencies, a larger fraction of the input mechanical energy is transferred to the mechanical-to-electrical conversion section of the harvester and, therefore, to the final user. A complete device design is proposed in this paper by taking into account a dedicated fabrication process which allows to obtain large inertial masses; electrostatic conversion has been considered and embedded into the device to evaluate the device performances in terms of the electric energy scavenged.

Nonlinear mechanism in MEMS devices for energy harvesting applications

This paper reports a novel bistable microelectromechanical system for energy harvesting applications. In particular, we focus here on methodologies and devices for recovering energy from mechanical vibrations. A common energy harvesting approach is based on vibrating mechanical bodies that collect energy through the adoption of self-generating materials. This family of systems has a linear mass–spring damping behaviour and shows good performance around its natural frequency. However, it is not generally suitable for energy recovery in a wide spectrum of frequencies as expected in the vast majority of cases when ambient vibrations assume different forms and the energy is distributed over a wide range of frequencies. Furthermore, whenever the vibrations have a low frequency content the implementation of an integrated energy harvesting device is challenging; in fact large masses and devices would be needed to obtain resonances at low frequencies. Here, the idea is to consider the nonlinear behaviour of a bistable system to enhance device performances in terms of response to external vibrations. The switching mechanism is based on a structure that oscillates around one of the two stable states when the stimulus is not large enough to switch to the other stable state and that moves around the other stable state as soon as it is excited over the threshold. A response improvement can be demonstrated compared to the classical linear approach. Indeed, both a wider spectrum will appear as a consequence of the nonlinear term and a significant amount of energy is collected at low frequencies. In this paper the bistable working principle is first described and analytically modelled, and then a numerical study based on stochastic differential equations (SDE) is realized to evaluate the behaviour of a MEMS device. A micromachined SOI prototype has been realized and a measurement campaign validated the nonlinear mechanism. As expected, the study shows that the nonlinear system exhibits a low pass filter behaviour suitable for harvesting ambient energy at low frequency.

The Evolution of MEMS Displays

Due to the advancement of microoptoelectromechanical systems and microelectromechanical systems (MEMS) technologies, novel display architectures have emerged. One of the most successful and well-known examples is the Digital Micromirror Device from Texas Instruments, a 2-D array of bistable MEMS mirrors, which function as spatial light modulators for the projection display. This concept of employing an array of modulators is also seen in the grating light valve and the interferometric modulator display, where the modulation mechanism is based on optical diffraction and interference, respectively. Along with this trend comes the laser scanning display, which requires a single scanning device with a large scan angle and a high scan frequency. A special example in this category is the retinal scanning display, which is a head-up wearable module that laser-scans the image directly onto the retina. MEMS technologies are also found in other display-related research, such as stereoscopic (3-D) displays and plastic thin-film displays.

Q2S2: A New Methodology for Merging Quantitative and Qualitative Information in Experimental Design

Sequential sampling refers to a set of experimental design methods where the next sample point is determined by information from previous experiments. This paper introduces a new sequential sampling method where optimization and user knowledge are used to guide the efficient choice of sample points. This method combines information from multiple sources of varying fidelity including actual physical experiments, computer simulation models of the product, and first principles involved in design and designer’s qualitative intuition about the design. Both quantitative and qualitative information from different sources are merged together to arrive at a new sampling strategy. This is accomplished by introducing the concept of a confidence function C, which is represented as a field that is a function of the decision variables x and the performance parameter f. The advantages of the approach are demonstrated using different example cases. The examples include design of a bistable microelectro mechanical system switch, a complex and relevant mechanical system.

Bistable microelectromechanical system based structures, systems and methods

A bistable microelectromechanical system (MEMS) based system comprises a micromachined beam having a first stable state, in which the beam is substantially stress-free and has a specified non-linear shape, and a second stable state. The curved shape may comprises a simple curve or a compound curve. In embodiments, the boundary conditions for the beam are fixed boundary conditions, bearing boundary conditions, spring boundary conditions, or a combination thereof. The system may further comprise an actuator arranged to move the beam between the first and second stable states and a movable element that is moved between a first position and a second position in accordance with the movement of the beam between the first and second stable states. The actuator may comprise one of a thermal actuator, an electrostatic actuator, a piezoelectric actuator and a magnetic actuator. The actuator may further comprise a thermal impact actuator or a zippering electrostatic actuator.

Modeling and experimental characterization of the chevron-type bi-stable microactuator

A compliant bi-stable micromechanism allows two stable states within its operation range to remain at one of the local minimum states of potential energy. Bi-stable energy characteristics offer two distinct and repeatable stable states that require no power input to maintain. In this paper we suggest a new theoretical model of the chevron-type bi-stable microactuator using equivalent stiffness in the rectilinear and rotational directions. From this model, the range of the spring stiffness in which the bi-stable mechanism can be operated is analyzed and compared with the results of finite element analysis (FEA) for buckling analysis. The analysis of the equivalent stiffness model shows that the forces necessary for the forward and backward actuation are almost linearly proportional to the equivalent stiffness, also in agreement with that of FEA. Based on the analysis, a novel chevron-type bi-stable microelectromechanical systems (MEMS) actuator with hinges and coupling bars is proposed for the improvement of a stable latch-up operation. The thickness and orientation of the hinge is determined through FEA in the light of reliable operation, stroke requirement, mechanical stress, and process constraint. The change in the cross-sectional area during the fabrication process is also considered to take into account its effects on the reduction of equivalent stiffness of the bi-stable MEMS actuator. The fabricated chevron-type microactuator showed a reliable bi-stable operation with a 60 µm stroke at 36 V input voltage, in agreement with the results of the equivalent stiffness model. Therefore, these results confirm that the chevron-type bi-stable MEMS actuator using hinges with coupling bars is applicable to optical switches.

RF MEMs variable capacitors for tunable filters

An RF MEMs (microelectromechanical system) variable capacitor has been demonstrated with a 22:1 tuning range, tuning from 1.5 to 33.2 pF of capacitance. This capacitor was constructed using bistable MEMs membrane capacitors with individual tuning ranges of 70:1 to 100:1, control voltages in the 30–55 V range, switching speeds less than 10 μS, and operating frequencies as high as 40 GHz. These devices may eventually provide a viable alternative to electronic varactors with improved tuning range and lower loss. ©1999 John Wiley & Sons, Inc. Int J RF and Microwave CAE 9: 362–374, 1999.

Chaos in MEMS, parameter estimation and its potential application

In this paper we present theoretical analysis and experimental results on the dynamic behavior of a bistable microelectromechanical systems (MEMS) oscillator, demonstrate the existence of a strange attractor in the MEMS device, and perform model verification using the experimental data. Secure communication schemes based on synchronized chaos are also applied to the device and successfully performed in the simulation.