Dynamical characteristics of fluid-conveying microbeams actuated by electrostatic force

In this paper, the dynamic characteristics and pull-in instability of electrostatically actuated microbeams which convey internal fluids are investigated. A theoretical model is developed by considering the elastic structure, laminar flow and electrostatic field to characterize the dynamic behavior. In addition, the energy dissipation induced by the fluid viscosity is studied through analyzing the fluid–structure interactions between the laminar fluid flow and oscillating microbeam by comprehensively considering the effects of velocity profile and fluid viscosity. The results indicate that the system is subjected to both the pull-in instability and the fluid-induced instability. It is demonstrated that as the flow velocity increases, both the static pull-in voltage and the dynamic one decrease for clamped–clamped microbeams while increase for clamped-free microbeams. It is also shown that the applied voltage and the steady flow can adjust the resonant frequency. The perturbation viscous flow caused by the vibration of microbeam is manifested to result in energy dissipation. The quality factor decreases with the increment of both the mode order and flow velocity. However, when the oscillating flow dominates, the flow velocity has no obvious effect.     

A resonant microstructure tunability analysis for an out-of-plane capacitive detection MEMS magnetometer

In this paper, the method of tuning the resonant frequency of a micro-resonant clamped–clamped beam has been successfully applied to a MEMS capacitive magnetometer. The resonant structure frequency, which presents the vital component of the sensor, was tuned by applying a bias voltage between the interdigitated capacitive comb-fingers in order to control its spring constant. It has been proved that an applied DC voltage increases the structure stiffness and as a result the resonance frequency to higher values, especially for low motion magnitude. The shifting causes were described through an accurate analytic analysis using the generated electrostatic force between movable and fixed combs, and thereafter have been proved by characterization. The measured resonance frequency of the clamped–clamped beam structure was changed by up to 38 % from the original value (around 18.2 kHz) when a bias voltage of 52 V was applied. Tuning the resonant frequency of the resonating structure has many advantages for the magnetometer since it can serve as a feedback mechanism for error compensation.

     

An innovative piezoelectric energy harvester using clamped–clamped beam with proof mass for WSN applications

In this paper a miniature piezoelectric energy harvester (PEH) with clamped–clamped beam and mass loading at the center is introduced which has more consistency against off-axis accelerations and more efficiency in comparison to other cantilever PEH’s. The beams consist of different layers of Si, piezoelectric, and insulators based on MEMS technology that vibrates by applying an external force to the fixed frame. Due to beam vibration, variable stress is applied to the AlN piezoelectric and a potential difference is created at the output terminals. AlN is deposited on clamped–clamped beams in such a way that produce more stress points which cause more power to be generated in comparison to other cantilever beam PEH’s with about same dimensions. A partial differential equations (PDE) describing the flexural wave propagating in the multi-morph clamped–clamped beam are solved as theoretical calculations for inherent frequency estimation and is confirmed by simulation results. The obtained inherent frequency is 42 Hz which with 1 g (g = 9.81 m/s²) acceleration produces 4 V and 80 µW maximum electrical peak power that can be used in the node of low-power consumption wireless sensor node for wireless sensor network (WSN) applications.

     

High-fidelity modeling of MEMS resonators. Part II. Coupled beam-substrate dynamics and validation

A computational multiphysics model of the coupled beam-substrate-electrostatic actuation dynamics of MEMS resonators has been developed for the model-based prediction of Q-factor and design sensitivity studies of the clamped vibrating beam. The substrate and resonator beam are modeled independently and then integrated by enforcing their interface compatibility condition and the force equilibrium to arrive at the multiphysics model. The present model has been validated with several reported single-beam clamped resonators. The validated model indicates that: the anchor loss is primarily engendered through coupling between the resonant modes and the waves propagating through the substrate inner layers; the resonant frequency of the beam decreases up to 5% due to substrate flexibilities interacting with beam at the anchors; and, for a given design the beam mass and its relative compliance with respect to the substrate are key parameters that influence the Q-factor degradation. In addition, the coupled model has also been used to predict the Q-factor of a paired-beam mechanical filter device with high fidelity when compared with the experimentally observed Q-factor.     

Modeling of the intrinsic stress effect on the resonant frequency of NEMS resonators integrated by beams with variable cross-section

Nano-electro-mechanical systems (NEMS) resonators integrated by a double clamped beam with variable cross-section are used in several applications such as chemical and biological detectors, high-frequency filters, and signal processing. The structure of these resonators can experience intrinsic stresses produced during their fabrication process. We present an analytical model to estimate the first bending resonant frequency of NEMS resonators based on a double clamped beam with three cross-sections, which considers the intrinsic stress effect on the resonant structure. This model is obtained using the Rayleigh and Macaulay methods, as well as the Euler–Bernoulli beam theory. We applied the analytical model to a silicon carbide (SiC) resonator of 186 nm thickness reported in the literature. This resonator has a total length ranking from 80 to 258 μm and is subjected to a tensile intrinsic stress close to 110 MPa. Results from this model show good agreement with experimental results. The analytic frequencies have a maximum relative difference less than 6.3% respect to the measured frequencies. The tensile intrinsic stress on the resonant structure causes a significantly increase on its bending resonant frequency. The proposed model provides an insight into the study of the intrinsic stress influence on the resonant frequency of this nanostructure. In addition, this model can estimate the frequency shift due to the variations of the resonator geometrical parameters.     

Mechanical design and characterization of a resonant magnetic field microsensor with linear response and high resolution

A resonant magnetic field microsensor based on Microelectromechanical Systems (MEMS) technology including a piezoresistive detection system has been designed, fabricated, and characterized. The mechanical design for the microsensor includes a symmetrical resonant structure integrated into a seesaw rectangular loop (700 μm × 450 μm) of 5 μm thick silicon beams. An analytical model for estimating the first resonant frequency and deflections of the resonant structure by means of Rayleigh and Macaulay's methods is developed. The microsensor exploits the Lorentz force and presents a linear response in the weak magnetic field range (40–2000 μT). It has a resonant frequency of 22.99 kHz, a sensitivity of 1.94 V T^?1, a quality factor of 96.6 at atmospheric pressure, and a resolution close to 43 nT for a frequency difference of 1 Hz. In addition, the microsensor has a compact structure, requires simple signal processing, has low power consumption (16 mW), as well as an uncomplicated fabrication process. This microsensor could be useful in applications such as the automotive sector, the telecommunications industry, in consumer electronic products, and in some medical applications.     

Effects of slots on thermoelastic quality factor of a vertical beam MEMS resonator

Thermoelastic damping is one of the dominant mechanisms of structural damping in vacuum-operated microresonators. A three dimensional numerical model based on the finite element method is used for simulating thermoelastic damping in clamped–clamped microelectromechanical beam resonators. In this regards, both simple and slotted beam are considered. To understand the effect of slot positions and sizes on the resonator performance, resonant frequency and thermoelastic quality factor are calculated for both simple and slotted beams for a wide range of beam length from 10 to 400 µm. Punching slots in the resonator beam reduces the stiffness and mass of the beam which affect the resonant frequency. In addition thermo-mechanical coupling mechanisms of the resonator are affected by the slots which improve the thermoelastic quality factor. For most of the beam lengths, it is shown that the slots at the beam-anchor interface region, where the strain is high, are more effectively enhanced the thermoelastic quality factor than one at the centre of the beam region. However, the highest resonance frequency is achieved with the slots at the center region.     

RF MEMS switches fabrication by using SU-8 technology

In this paper we present a novel process based on SU-8 technology for the fabrication of double clamped radio frequency (RF) micro-electro-mechanical system (MEMS) capacitive shunt switches in coplanar configuration. The key element of the exploited process is the MicroChem SU-8 2002 negative photoresist. The polymeric material is widely used in MEMS device processes because of its excellent thermal and chemical stability. In this paper, SU-8 polymer has been utilized in a double way to get suspended structures as double clamped beams: (1) SU-8 for the lateral supports, and (2) as a sacrificial layer for the release of the suspended membrane. Preliminary RF tests on the manufactured switches have been done, and the measured electrical performances are in good agreement with the performed simulations.     

Realisation and characterisation of mass-based diamond micro-transducers working in dynamic mode

We report on novel MEMS micro-transducers made of diamond and targeted for bio-sensing applications. To overcome the non-straightforward micromachining of diamond, we developed a bottom up process for the fabrication of synthetic diamond micro-structures involving the patterned growth of diamond using the CVD (chemical vapour deposition) technique, inside micro-machined silicon moulds. Here typical resonant MEMS structures including cantilevers fabricated using this method were characterized by measuring their first mode resonance (frequency and Q-factor) by Doppler laser interferometry. The experimental data matched the simulation data. Data from bare diamond cantilevers and from diamond cantilevers with actuation gold track on the surface were compared and showed a significant decrease in the resonant frequency in the presence of gold tracks. Nevertheless, comparisons with equivalent silicon structures demonstrated the superior performances of diamond cantilevers: the resonance frequencies were twice higher and the Q-factors 2.5 times higher for the diamond transducers. Diamond cantilevers sensitivity were measured using PMMA deposition and values as high as 227.4 Hz ng⁻¹ were found. It was shown that diamond mass sensitivity values are typically two times higher than identical silicon devices. Finally, the limit of detection (LOD) of diamond cantilevers was found experimentally to be as low as 0.86 pg using our set up. This is suitable for many bio-sensing applications.     

Design and optimization of RF ICs with embedded linear macromodels of multiport MEMS devices

In this paper, we demonstrate efficient modeling approach for simulation, analysis, design, and optimization of multiport radio frequency microelectromechanical systems (RF MEMS) resonating structures embedded in RF circuits. An in‐house finite element method (FEM) solver is utilized to develop accurate and efficient macromodels that capture all the essential characteristics of the device. Using the datasets generated from the FEM simulations, the artificial neural network models are trained for two‐way mapping between the physical input and electrical output parameters. Realized model is implemented in a circuit simulator, enabling a simple yet accurate circuit simulator compatible modeling and optimization procedure instead of memory and time demanding FEM analysis. The derivation of dynamic macromodels with preserved electromechanical behavior of the multiport resonating structures is also presented. Capabilities of the proposed approach are demonstrated with several examples featuring capacitively actuated MEMS resonating structures: a clamped–clamped beam, a free–free beam, and a coupled clamped–clamped beam. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.     

Electronically probed measurements of MEMS geometries

Measurement of microelectromechanical systems (MEMS) geometry is critical for device design and simulation, material property extraction, and post-fabrication trimming. In this paper electrostatically driven laterally resonant comb-drive test structures with prescribed changes in spring width are used to ascertain systematic variations in process offsets (edge biases) and sidewall angles. The technique is both in situ and nondestructive. An analytical model for the resonant frequency, tuned with three-dimensional (3-D) simulations using MEMCAD, includes effects of a distributed mass, residual stress, and compliant supports. The model is corroborated by 3-D numerical simulations to validate the extraction approach. Fits of this model to experimental data determine the offset and sidewall angle of polysilicon devices fabricated by the Multi-User MEMS Processes of the Microelectronics Center of North Carolina, Research Triangle Park, NC     

Response of thermoelastic microbeams to a periodic external transverse excitation based on MCS theory

Microsystem Technologies - In this paper, we investigated the dynamics vibration of clamped–clamped microbeams exposed to associate exterior cross excitation. The theory of modified couple...     

Partitioning design space for linear tuning of natural frequencies in planar dynamic MEMS structures

One of the critical design considerations in dynamic microelectromechanical systems (MEMS) devices is the structural natural frequency of the sensing or actuation element. Most dynamic MEMS devices employ planar geometry using an assembly of beams and plates for the structural elements. Most often the goal is to place the first resonant frequency at a desired value. Since the frequency depends on mass and stiffness of the structure, designing for frequency usually requires FEM analysis of the structure. FEM calculations are intensive, depend on many subtle modelling assumptions, and require huge number of simulations to build intuition. Since the design space for such structures is fairly high dimensional, tuning the frequency of the first-cut design can be a fairly intensive optimization computation. Here, we present a lumped parameter spring-mass model for a typical microstructure consisting of a plate and beams and show how the higher dimensional geometric design space can be partitioned to effect desired frequency changes in the structure linearly with the chosen design variables. In particular, four sets of design variables are considered and their effective range and sensitivity for linear tuning of the natural frequency is presented. We include the effect of residual stress on stiffness and show how the values of residual stress affect the tuning of the natural frequency with respect to the selected design variables. All results are compared with FEM calculations and a table is presented for cross comparison of efficacy of the different design variables. The goal is to present a simple analysis that can be easily followed by MEMS designers with any background and build their intuition for such designs.     

Vibrations of shear deformable FG viscoelastic microbeams

This is the first paper which investigates the nonlinear forced dynamic response of shear deformable functionally graded (SDFG) microscale beams with viscoelastic properties. A third-order model of shear deformations, which satisfies both the lower and upper boundary conditions, is utilised. The influences of viscoelastic properties are incorporated via the Kelvin–Voigt scheme. Furthermore, the influences of being at a miniature scale are captured via a modified couple stress theory (MCST). The material distribution of the microsystem is modelled via application of the Mori–Tanaka approach. Nonlinear three-dimensional coupled equations, which govern the size-dependent motions of the SDFG microbeam, are derived and then numerically solved. The present results show that for large coupled motions, the nonlinearity caused by viscosity plays a crucial role in the dynamics of SDFG microbeams.

     

Design considerations for an acoustic MEMS filter

Microelectromechanical system (MEMS) devices exhibit characteristics that make them ideal for use as filters in acoustic signal processing applications. In this study, a MEMS filter is constructed from multiple mechanical structures (e.g. cantilever beams) and a differential amplifier. The outputs of the structures are then processed by the differential amplifier to achieve the filter functionality. The important parameters of the mechanical structures and the MEMS filters are investigated using a simulation approach, including the structural damping factors, the normalized frequency ratios (NFR) of the MEMS filters, the number of mechanical structures required to construct individual MEMS filter, and the spatial arrangement of the multiple mechanical structures relative to the differential amplifier. Furthermore, the mutual coupling effects among these parameters are evaluated by detailed simulations. The simulation results show that a plot of the NFR versus the damping factors can be used to determine the optimal parameters for the mechanical structures. The number of mechanical structures required to construct a MEMS filter must equal 2ⁿ, with n as an integer, and these mechanical structures should be arranged as a geometric series with increasing resonant frequencies and with specific connections to the differential amplifier.This material is based (in part) upon work supported by the National Science Council (Taiwan) under Grant NSC 91–2213-E-010-008 and Delta Electronics Foundation. The authors would like to express their appreciation to the NSC Central Regional MEMS Center, Semiconductor Research Center of National Chiao Tung University (Taiwan), and the NSC National Nano Device Laboratories (Taiwan) in providing experimental facilities.     

A miniature in-plane piezoresistive MEMS accelerometer for detection of slider off-track motion in hard disk drives

A miniature in-plane pizoresistive MEMS accelerometer was designed, fabricated and characterized for detection of slider off-track motion in hard disk drives. The structure of the accelerometer consists of a central supporting beam and two stress-magnifying sensing beams. Under geometric constraints imposed by the trailing side of a pico slider, the accelerometer design was optimized to achieve approximately pure axial deformation in the sensing beams and a maximum sensitivity with a specified natural frequency of 300 kHz. Fabricated on a silicon-on-insulator (SOI) wafer, the accelerometer with a half Wheatstone bridge was wirebonded to external pads and interfaced with an amplifier circuit on a printed circuit board (PCB). The noise level, sensitivity, nonlinearity were characterized with vibration testing on a shaker. The miniature accelerometer (1 × 0.3 × 0.3 mm³) with a weight of only 0.2 mg offers a much higher resonant frequency with a comparable sensitivity compared with those in previous work.     

An investigation into the electrostatic force representation for electrically actuated microelectromechanical systems

The ever-increasing demand for microelectromechanical systems (MEMS) in modern electronics has reinforced the need for extremely accurate analytical and reduced-order models to aid in the design of MEMS devices. Many MEMS designs consist of cantilever beams with a tip mass attached at the free end to act as a courter electrode for electrical actuation. One critical modeling aspect of electrically actuated MEMS is the electrostatic force that drives these systems. The two most used representations in the literature approximate the electrostatic force between two electrodes as a point force. In this work, the effects of the representation of the electrostatic force for electrically actuated microelectromechanical systems are investigated. The system under investigation is composed of a beam with an electrode attached to its end. The distributed force, rigid body, and point mass electrostatic force representations are modeled, studied, and their output results are compared qualitatively. Static and frequency analyses are carried out to investigate the influences of the electrostatic force representation on the static pull-in, fundamental natural frequency, and mode shape of the system. A nonlinear distributed-parameter model is then developed in order to determine and characterize the response of electrically actuated systems when considering various representation of the electrostatic forces. The results show that the size of the electrode may strongly affect the natural frequencies and static pull-in when the point mass, rigid body, and plate representations are considered. From nonlinear analysis, it is also proven that the representation may affect the hardening behavior of the system and its dynamic pull-in. This modeling and analysis give guidelines about the usefulness of the electrostatic force representations and possible erroneous assumptions that can be made which may result in inaccurate design and optimal performance detection for electrostatically actuated systems.

     

Architectures for vibration-driven micropower generators

Several forms of vibration-driven MEMS microgenerator are possible and are reported in the literature, with potential application areas including distributed sensing and ubiquitous computing. This paper sets out an analytical basis for their design and comparison, verified against full time-domain simulations. Most reported microgenerators are classified as either velocity-damped resonant generators (VDRGs) or Coulomb-damped resonant generators (CDRGs) and a unified analytical structure is provided for these generator types. Reported generators are shown to have operated at well below achievable power densities and design guides are given for optimising future devices. The paper also describes a new class-the Coulomb-force parametric generator (CFPG)-which does not operate in a resonant manner. For all three generators, expressions and graphs are provided showing the dependence of output power on key operating parameters. The optimization also considers physical generator constraints such as voltage limitation or maximum or minimum damping ratios. The sensitivity of each generator architecture to the source vibration frequency is analyzed and this shows that the CFPG can be better suited than the resonant generators to applications where the source frequency is likely to vary. It is demonstrated that mechanical resonance is particularly useful when the vibration source amplitude is small compared to the allowable mass-to-frame displacement. The CDRG and the VDRG generate the same power at resonance but give better performance below and above resonance respectively. Both resonant generator types are unable to operate when the allowable mass frame displacement is small compared to the vibration source amplitude, as is likely to be the case in some MEMS applications. The CFPG is, therefore, required for such applications.     

Comparison analysis of energy loss between micro clamped–clamped and clamped-free beam in vertical motion flux modulation magnetic sensor

The 1/f noise is one of the main noise sources of giant magnetoresistive sensors, which will cause intrinsic detection limit at low frequency. To suppress this noise, a vertical motion flux modulation (VMFM) integrated with simple microelectromechanical-systems (MEMS) structure is proposed. However, the energy loss of VMFM structure is not considered yet. In this paper, energy loss between MEMS clamped–clamped beam (C–C beam) and clamped-free beam (C-F beam) used as VMFM structure are compared. In this comparison, quality factor (Q) is proposed to characterize the energy loss of the VMFM structure. Theory analysis and experimental results show that quality factor of a C–C beam is higher than that of a C-F beam, indicating a lower energy in VMFM. Finally, the sensitivity of a VMFM magnetic sensor modulated by a C–C beam is tested, and the sensitivity gets 3.85 mV/V/Gs.

     

Design and modeling of a novel microsensor to detect magnetic fields in two orthogonal directions

In this paper, we present the design and modeling of the electrical–mechanical behavior of a novel microsensor to detect magnetic fields in two orthogonal directions (2D). This microsensor uses a simple silicon resonant structure and a Wheatstone bridge with small p-type piezoresistors (10 × 4 × 1 μm) to improve the microsensor resolution. The resonant structure has two double-clamped silicon beams (1000 × 28 × 5 μm) and an aluminum loop (1 μm thickness). The microsensor design allows important advantages such as small size, compact structure, easy operation and signal processing, and high resolution. In addition, the microsensor design is suitable to fabricate using silicon on insulator (SOI) wafers in a standard bulk micromachining process. An analytical model is developed to predict the first bending resonant frequency of the microsensor structure using Macaulay and Rayleigh methods, as well as the Euler–Bernoulli beam theory. Air and intrinsic damping sources of the microsensor structure are considered for its electrical–mechanical response. The mechanical behavior of the microsensor is studied using finite element models (FEMs). For 10 mA of root mean square (RMS) excitation current and 10 Pa air pressure, this microsensor has a linear electrical response, a fundamental bending resonant frequency of 52,163 Hz, and a high theoretical resolution of 160 pT.