Slide-film Damping Research Articles

Cavity-Depth Effect on 3D Wafer-Level-Packaged MEMS Resonators by Slide-Film Damping

Cavity-Depth Effect on 3D Wafer-Level-Packaged MEMS Resonators by Slide-Film Damping

Noise multiplication and bandwidth of photodetectors employed with Taylor dispersion in micro optical fiber channel system

Abstract This work has clarified the noise multiplication and bandwidth of photodetectors employed with Taylor dispersion in micro optical fiber channel system. The simulation performance evaluation of slide and squeeze film damping and fluidics mechanics. The damping ratio versus gap distance for a cantilever beam and a mass suspended from beams are determined. The damping ratio with gap size for a suspended mass with and without holes is reported. The damping ratio variations with the gap distance variations for a mass suspended from beams is clarified. The velocity field for fluid flow in a circular channel, a square channel, a rectangular channel, a parabolic channel and a triangular channel is estimated. Besides the velocity field for the fluid flow in a channel with and without slip is outlined. The spreading of a diffusion front in one dimension in a resting fluid and the dispersion coefficient in a square channel [Taylor dispersion in micro fluidic channels] are clarified. The 2D diffusion profile of a solute in a T mixer and normalized concentration versus the channel width for the solute at the outlet of H filter are determined.

The quality factor of quartz DETF for resonant sensors: simulation, analysis and verification

Due to the excellent material properties of crystal quartz and its simple and effective structure, the quartz double ended tuning fork (DETF) is widely used as a resonance sensing element in resonator sensors, where its quality factor has an important effect on the overall accuracy and stability of such sensors. To optimise the quality factor of quartz DETF, the influence of structural dimensions on structural and air damping is analysed, and the theoretical model used to calculate the quality factor is summarised. Further, under the premise of fabricating resonators with sufficient force–frequency sensitivity, the quality factors of quartz DETFs of different structural dimensions are simulated through finite element simulation. The theoretical model and simulation calculation of the quality factor of quartz DETFs mutually verify its effectiveness. Moreover, an experimental platform was built, and three quartz DETFs with different dimensions were fabricated to test their quality factor. The quality factors of the three DETFs in air and vacuum are 3467.3, 1925.8, 4442.4 and 32 997.6, 11 559.1, 24 795.7, respectively, which means that the environmental factors and their structural dimensions have a great influence on quality factor. With the simulation method and summarised theoretical model in this paper, the quality factor was studied with comprehensive structural damping (thermal damping loss and support loss) and air damping (resistance damping, slide film damping, and squeeze film damping). The influence of the structure size on the quality factor was analysed in detail, including the length of the decoupling region, the distance between the tines, and the length and width of the tines, and the main influencing factors were obtained, providing a basic and comprehensive reference for designing quartz DETF.

A Novel Biosensor Based on Micromechanical Resonator Array for Lab-On-a-Chip Applications

Mechanical resonators are rarely reported to be used in liquid environment due to high damping. Most applications of mechanical resonators are related to their use in the gaseous environment. In this paper, a novel mass detective biosensor is proposed for Lab-On-a-Chip applications based on micromechanical resonator array. The sensor can be fabricated by MEMS technology such as standard Polysilicon Multi User MEMS Process (PolyMUMPs). The sensor consists of chained mechanically coupled resonators with electrostatic actuating elements and capacitive sensing elements on both sides. The sensor is suitable for digital microfluidic applications which an under test droplet can be led over the resonator array and affect the frequency or the phase delay of vibration. Thus, both sides of the array containing the actuating and sensing elements stay away from the droplet. It provides conditions that do not electrically interfere with the sample droplet. The vibration direction of resonators under liquid droplet is such that causes light slide film damping and does not cause strong squeeze film damping. The commercial finite element tool COMSOL Multiphysics is used to analyze the vibration behavior of proposed sensor and verify its functionality. The results are presented for the frequency response and mass sensitivity of the biosensor.

MRT-LBM modelling of the oscillatory gas slide film damping in the transition regime

In this paper, the slide film damping (SFD) of micro-scale oscillatory Couette flow has been researched by an effective multiple relaxation time lattice Boltzmann method (MRT-LBM). The validity and effectiveness of MRT-LBM for solving SFD have been verified through contrasting the velocity distribution between the upper plate and the substrate of MRT-LBM and the direct simulation Monte Carlo (DSMC) model. The impacts of the vibration frequency and gap of plates on the damping are discussed, and the result shows that the nonlinear character of velocity profiles is manifest and SFD increases substantially for a larger vibration frequency in the oscillatory gas flow; SFD reduces obviously with the gap increases. Consequently, the results further confirm the implementation of LBM in analysis of the non-equilibrium micro-scale gas flow.

A Universal High-Sensitivity Area-Variation Capacitive Displacement Transducer (CDT) Based on Fringe Effect

Capacitive displacement transducers (CDTs) have been widely used in many physical sensors, attributing to high-resolution, simple electricity and easy manufacturing process. Gap-variation CDTs generally have higher displacement resolution due to small electrode gaps but suffer from the pull-in effect, the nonlinear effect and squeeze-film damping; whereas area-variation CDTs have intrinsically good linearity and much smaller slide-film damping. However, the parallel-plate-based area-variation CDTs have the electrode width much larger than the electrode gap with negligible fringe effect; therefore, the sensitivity is limited by periodic electrode numbers. In this paper, we introduce a novel fringe-effect dominated area-variation CDT with a much higher sensitivity within a certain electrode-deployable area. Both theoretical and numerical analysis are applied to investigate the working principle of the CDT design. The proposed fringe-effect-based CDT benefits from a much larger capacitance-to-displacement sensitivity than the traditional periodic array parallel-plate-based CDT, due to the more displacement-sensitive fringe field and more deployable electrode periods. A set of experiments are designed, and the proposed area-variation CDTs are evaluated. Experimental results suggested that the proposed CDT design, which had equal electrode width, separation and gap, could universally be applied to sensors with different featured dimensions either in macroscale or microscale. Angular misalignments with both out-of-plane tilts and in-plane rotations, which affect the output offset and sensitivity, should be minimized or alleviated. The proposed fringe-effect-based CDT are successfully applied to a single-axis in-plane sensing micro-electromechanical systems (MEMS) accelerometer, showing a noise floor as low as 0.25 ng/Hz 1/2 @1 Hz. The corresponding displacement noise of the proposed CDT is 0.1 pm/Hz 1/2 .

Z-axis tuning fork gyroscope having a controlled anti-phase and freestanding architecture: design and fabrication

This paper reports the design and fabrication of a z-axis tuning fork gyroscope (TFG) having anti-phase controlled and freestanding architectures. The gyroscope is designed to suppress the in-phase sensing mode by using a self-rotation ring. To improve the performance of the TFG by limiting the influence of the squeeze-film damping, the driving and sensing parts of the gyroscope were designed to oscillate in plane. Furthermore, by removing the substrate underneath the device, the slide-film damping in the gap between the proof masses and the substrate is eliminated. The proposed architecture is analysed by finite element method using ANSYS software. The simulated frequencies of the driving and sensing modes are 9.788 kHz and 9.761 kHz, respectively, which determines the sensor bandwidth of 27 Hz. The frequency difference between the driving and sensing modes and the parasitic ones is obtained to be 57.5%. The sensing displacement and driving displacement of the gyroscope at resonance are 0.104 μm and 6.034 μm, respectively. The gyroscope was fabricated based on the bulk micromachining technology. It is shown that the quality factor of the gyroscope is 111.2. The measured sensitivity of the sensor is evaluated to be 11.56 mV/°/s.

Experimental Analysis of the Gas Film Damping Effect in an Aerostatic Guideway under Microscale

ABSTRACTThis article studies the mechanism of gas film damping on the aerostatic guideway system at a microscale with the modified Reynolds equation. The slide film damping force due to the fluid viscous effect is calculated, and the squeeze damping force caused by the gas compression and escape between two plates is analyzed. The damping ratio in the calculation model for the slide film damping is compared with the calculated results from the experiment and the finite element analysis results. Using the results of the study, the optimal supply pressure is designed. The method applied in this article provides the theoretical basis for the analysis and solution of the dynamic performance of an aerostatic guideway.

Modal Analysis of a Single-Structure Multiaxis MEMS Gyroscope

This paper reports on designing a single-structure triaxes MEMS capacitive gyroscope which is capable of measuring the three angular velocities on a single drive. A Z-shaped beam for the support of folded coupling spring has been applied to suppress the unwanted mode and decrease the stress effect at the spring ends. The unique coupling spring has changed the driving motion, due to which slide film damping in the driving mode has been reduced. This reduction can lead to higher performance of the sensor with less requirements on vacuum level which decreases the cost of fabrication. Simulation analysis has been performed in COMSOL Multiphysics and Matlab Simulink to finalize the design for fabrication. After finite element analysis, the driving, x-sensing, z-sensing, and y-sensing are, respectively, found to be 13.30 KHz, 13.40 KHz, 13.47 KHz, and 13.51 KHz.

A high performance micro-pressure sensor based on a double-ended quartz tuning fork and silicon diaphragm in atmospheric packaging

A resonant micro-pressure sensor based on a double-ended quartz tuning fork (DEQTF) and bossed silicon diaphragm in atmospheric packaging is presented. To achieve vacuum-free packaging with a high quality factor, the DEQTF is designed to resonate in an anti-phase vibration mode in a plane that is under the effect of slide-film damping. The feasibility is demonstrated by theoretical analysis and a finite element simulation. The dimensions of the DEQTF and diaphragm are optimized in accordance with the principles of improving sensitivity and minimizing energy dissipation. The sensor chip is fabricated using quartz and silicon micromachining technologies, and simply packaged in a stainless steel shell with standard atmosphere. The experimental setup is established for the calibration, where an additional sensor prototype without a pressure port is introduced as a frequency reference. By detecting the frequency difference of the tested sensor and reference sensor, the influences of environmental factors such as temperature and shocks on measuring accuracy are eliminated effectively. Under the action of a self-excitation circuit, static performance is obtained. The sensitivity of the sensor is 299 kHz kPa−1 in the operating range of 0–10 kPa at room temperature. Testing results shows a nonlinearity of 0.0278%FS, a hysteresis of 0.0207%FS and a repeatability of 0.0375%FS. The results indicate that the proposed sensor has favorable features, which provides a cost-effective and high-performance approach for low pressure measurement.

Slide film damping in microelectromechanical system devices

Film damping caused by microfluids has important effects on the dynamic characteristics of moving elements of microelectromechanical system devices. There are two kinds of film damping existing in microelectromechanical system devices, for instance, slide film damping and squeeze film damping. This article presents an overview on the recent research progress on the slide film damping in microelectromechanical system devices. Based on the first slip velocity boundary conditions, this article discusses two kinds of damping models in detail, which commonly used to investigate on the slide film damping. For the convenience of quick reference in future, laterally moving microstructures, adequate important equations and applicable conditions are included in this article. Finally, we proposed two unified models for the analysis and design of laterally moving microstructured devices.

Analysis and Simulation of Two Hinged Ends Micro-Beam Relaxation Process

In order to explore micro-beam relaxation dynamics of MEMS, the beam deflection relaxation expression considering air slide-film damping effect was educed based on Euler–Bernoulli equation with boundary conditions of two hinged ends. The beam deflection relaxation process under over damping, critical damping and under damping was calculated used Maple. The relaxation simulation data of micro-beam with two hinged ends used ANSYS demonstrate that relaxation process conform to theoretical calculation and relaxation period of under damping relaxation approximate constant when damping coefficient is small, but increase significantly when damping coefficient is large.

Effect of air damping on quality factor of bulk mode microresonators

In this paper, the air damping effect on quality factor of bulk mode microresonators is analyzed and measured. Both the squeeze film damping and slide film damping are considered in the analysis procedure. The reactions of the resonant plate with the air flows in the transduction gaps and around the resonator plate surfaces are investigated based on the Reynolds equation and the Stoke-flow model, respectively. An electrical equivalent model has been derived for a microresonator operating in air, based on the squeeze film damping and slide film damping effect. The model is realized with resistors equivalent for the slide film damping force and frequency-dependent resistors and capacitances connected in series equivalent for the squeeze film damping force. Circuit analysis tool is employed to calculate the response of the microresonator. The simulated transmission characteristics are in good agreement with the experimental results. Consequently, this approach provides a method to estimate the effect of air damping on the dynamic response of the micromechanical devices.

Design and Simulation of Capacitive Micromechaned Gyroscope

By researching and investigating the structure of capacitive gyroscopes, A novel capacitive micromachined gyroscope is proposed and the structure is designed. The method of electrostatic comber drive, capacitive detection of bar structure is used for the structure, and these make the gyroscope high sensitivity. The main air damping of the drive mode and detection mode is slide film damping, it is possible to make the gyroscope achieve high Q-values at atmospheric pressure. The decoupled gyroscope is designed, too. By large numbers of simulation analysis， frequencies of the first six steps mode are gained, nature frequencies of drive mode and sense mode of gyroscope are a close match, and rationality of the structure is validated. At last, the structure encapsulated is presented.

A Lateral-Axis Microelectromechanical Tuning-Fork Gyroscope With Decoupled Comb Drive Operating at Atmospheric Pressure

In this paper, a silicon bulk micromachined lateral-axis tuning-fork gyroscope (TFG) with a decoupled comb drive and torsional sensing comb capacitors is presented. The novel driving comb capacitors are used to suppress the parasitic out-of-plane electrostatic force and, hence, can decouple the mechanical crosstalk from the sensing mode to the driving mode in a simple manner. The torsional sensing combs are designed to differentially sense the out-of-plane rotational moment and are arranged centroidally to be immune to fabrication imperfections for good linearity and electrostatic force balancing. The torsional sensing combs adopted in the TFG help to lower the air damping of the sensing mode while the driving mode of the gyroscope is dominated by slide-film air damping; hence, it can work even at atmospheric pressure. The process for this lateral-axis gyroscope can also be used to fabricate z-axis gyroscopes; therefore, low-cost miniature monolithic inertial measurement units can be realized without vacuum packaging. The TFG is tested at atmospheric pressure with a sensitivity of 17.8 mV/°/s and a nonlinearity of 0.6% in a full-scale range of 1000°/s. The bias stability is measured to be 0.05°/s (1 ?) in 30 min with an equivalent noise angular rate of 0.02°/s/Hz1/2.

A novel electrostatic-driven tuning fork micromachined gyroscope with a bar structure operating at atmospheric pressure

A novel electrostatic-driven tuning fork micromachined gyroscope with a bar structure is presented. The gyroscope is fabricated by silicon–glass bonding and deep reactive ion etching (DRIE) technology. The gyroscope's driving and sensing proof masses consist of many movable bars. As the motion of the movable proof masses is parallel to the plane of fixed driving and sensing electrodes on a glass substrate, there is mainly slide film damping in the driving and sensing directions, which enables it to achieve high-quality factors and vacuum-free packaging. The gyroscope can operate at atmospheric pressure by electrostatic driving and capacitive sensing. The performances of the gyroscope are tested and the results show that the resonant frequencies and the quality factors for driving and sensing modes are 2.873 kHz and 2.989 kHz, 804 and 789 at atmospheric pressure, respectively. The scale factor and nonlinearity of the gyroscope are 17.45 mV/°/s and 0.43%, respectively.

An in-plane low-noise accelerometer fabricated with an improved process flow

We present a bulk micromachined in-plane capacitive accelerometer fabricated with an improved process flow, by etching only one-fifth of the wafer thickness at the back of the silicon while forming the bar-structure electrode for the sensing capacitor. The improved flow greatly lowers the footing effect during deep reactive ion etching (DRIE), and increases the proof mass by 54% compared to the traditional way, resulting in both improved device quality and a higher yield rate. Acceleration in the X direction is sensed capacitively by varying the overlapped area of a differential capacitor pair, which eliminates the nonlinear behavior by fixing the parallel-plate gap. The damping coefficient of the sensing motion is low due to the slide-film damping. A large proof mass is made using DRIE, which also ensures that dimensions of the spring beams in the Y and Z directions can be made large to lower cross axis coupling and increase the pull-in voltage. The theoretical Brownian noise floor is 0.47 µg/Hz1/2 at room temperature and atmospheric pressure. The tested frequency response of a prototype complies with the low damping design scheme. Output data for input acceleration from −1 g to 1 g are recorded by a digital multimeter and show very good linearity. The tested random bias of the prototype is 130 µg at an averaging time of around 6 s.

A novel MEMS inertial sensor with enhanced sensing capacitors

A novel MEMS inertial sensor with enhanced sensing capacitors is developed. The designed fabricated process of the sensor is a deep RIE process, which can increase the mass of the seismic to reduce the mechanical noise, and the designed capacitance sensing method is changing the capacitance area, which can reduce the air damping between the sensing capacitor plates and reduce the requirement for the DRIE process precision, and reduce the electronic noise by increasing the sensing voltage to improve the resolution. The design and simulation are also verified by using the FEM tool ANSYS. The simulated results show that the transverse sensitivity of the sensor is approximately equal to zero. Finally, the fabricated process based on silicon–glass bonding and the preliminary test results of the device for testing grid capacitors and the novel inertial sensor are presented. The testing quality factor of the testing device based on the slide-film damping effect is 514, which shows that the enhanced capacitors can reduce mechanical noise. The preliminary testing result of the sensitivity is 0.492 pf/g.

Process flow improvement on a bulk micromachined gyroscope

An introduction of a bulk micromachined frame gyroscope and the efforts made to lower the footing effect during deep reactive ion etching (DRIE) is featured. The gyroscope is driven into oscillation electrostatically and senses rate signal by the varying overlapped area of the electrodes, which eliminates the nonlinear behaviour of sensing the varying gap. Damping factors for the driving and sensing modes are low due to the slide-film damping, resulting in high quality factors in the atmosphere. A large proofmass can be made by DRIE, which also ensures a large pull-in voltage. The footing effect during fabrication has been greatly reduced by the improved process flow, which also increases the proof mass by 50%. Thus device quality and yield rate are both improved. Functional results of an improved prototype are given.

A novel capacitive micro-accelerometer with grid strip capacitances and sensing gap alterable capacitances

The comb capacitances fabricated by deep reactive ion etching (RIE) process have high aspect ratio which is usually smaller than 30: 1 for the complicated process factors, and the combs are usually not parallel due to the well-known micro-loading effect and other process factors, which restricts the increase of the seismic mass by increasing the thickness of comb to reduce the thermal mechanical noise and the decrease of the gap of the comb capacitances for increasing the sensitive capacitance to reduce the electrical noise. Aiming at the disadvantage of the deep RIE, a novel capacitive micro-accelerometer with grid strip capacitances and sensing gap alterable capacitances is developed. One part of sensing of inertial signal of the micro-accelerometer is by the grid strip capacitances whose overlapping area is variable and which do not have the non-parallel plate's effect caused by the deep RIE process. Another part is by the sensing gap alterable capacitances whose gap between combs can be reduced by the actuators. The designed initial gap of the alterable comb capacitances is relatively large to depress the effect of the maximum aspect ratio (30 : 1) of deep RIE process. The initial gap of the capacitance of the actuator is smaller than the one of the comb capacitances. The difference between the two gaps is the initial gap of the sensitive capacitor. The designed structure depresses greatly the requirement of deep RIE process. The effects of non-parallel combs on the accelerometer are also analyzed. The characteristics of the micro-accelerometer are discussed by field emission microscopy (FEM) tool ANSYS. The tested devices based on slide-film damping effect are fabricated, and the tested quality factor is 514, which shows that grid strip capacitance design can partly improve the resolution and also prove the feasibility of the designed silicon-glass anodically bonding process.