Squeeze-film Air Damping Research Articles

Accurate mechanical-optical theoretical model of cross-axis sensitivity of an interferometric micro-optomechanical accelerometer.

An interferometric micro-optomechanical accelerometer usually has ultrahigh sensitivity and accuracy. However, cross-axis interference inevitably degrades the performance, including its detection accuracy and output signal contrast. To accurately clarify the influence of cross-axis interference, a modified mechanical-optical theoretical model is established. The rotation of the proof mass and the detected light intensity are quantitatively investigated with a load of cross-axis acceleration. A simulation and experiment are performed to verify the correctness of the theoretical model when the cross-axis acceleration is from 0 to 0.175 g. The results demonstrate that this model has a more than fivefold accuracy increase compared with conventional theoretical models when the cross-axis acceleration is from 0.06 to 0.175 g. In addition, we provide a suppression method to diminish the rotation of the proof mass based on squeeze film air damping, which significantly suppresses the contrast reduction caused by cross-axis interference.

Correlated Theory of Cross-Axis Interference of MEMS Devices Based on Parallel Plate and Squeeze Film Air Damping Induced Suppression

Owing to inevitable errors of the material and fabrication process, the cross-axis sensitivity commonly exists in a large number of MEMS devices based on parallel plate structures. Such cross-axis interference results in the non-negligible rotation of the plate that deteriorates the performance of MEMS devices. Therefore, suppressing the cross-axis sensitivity is extremely critical in the device design. This paper proposes a novel theory to identify the interplay between the cross-axis interference and squeeze film air damping, and further develops a correlated theory of the damping induced suppression. The model of tilting plate with a tiny amplitude is set up by exploiting the Reynolds equation coupled with the equations of the mass deflection, and the analytical expressions of corresponding properties are derived to elucidate the suppression mechanism and its characterization. The analytical calculation and numerical simulation analysis demonstrate that the damping induced improvement effect exists objectively and is remarkable in the condition of a large mass and a small air film thickness. The cross-axis sensitivity rendered by the tilt angle quantitatively declines 80% in terms of the air damping. The theoretical underpinning can be utilized to elaborate the ubiquitous interplay between squeeze film air damping and cross-axis interference in non-vacuum MEMS devices, which is of paramount importance for achieving high performance and stability. More importantly, it is not an exclusive method that can be combined with other methods to minimize the cross-axis interference fully.

Extending the Validity of Squeeze Film Damping Models with Lower Aspect Ratios.

Squeeze film air damping is a significant factor in the design of MEMS devices owing to its great impact on the dynamic performance of vibrating structures. However, the traditional theoretical results of squeeze film air damping are derived from the Reynolds equation, wherein there exists a deviation from the true results, especially in low aspect ratios. While expensive efforts have been undertaken to prove that this deviation is caused by the neglect of pressure change across the film, a quantitative study has remained elusive. This paper focuses on the investigation of the finite size effect of squeeze film air damping and conducts numerical research using a set of simulations. A modified expression is extended to lower aspect ratio conditions from the original model of squeeze film air damping. The new quick-calculating formulas based on the simulation results reproduce the squeeze film air damping with a finite size effect accurately with a maximum error of less than 1% in the model without a border effect and 10.185% in the compact model with a border effect. The high consistency between the new formulas and simulation results shows that the finite size effect was adequately considered, which offers a previously unattainable precise damping design guide for MEMS devices.

A TRT-LBM model of squeeze film air damping of micro-beam in the transition regime

A TRT-LBM model of squeeze film air damping of micro-beam in the transition regime

Intermodal Brillouin scattering in solid-core photonic crystal fibers

We investigate intermodal forward Brillouin scattering in a solid-core photonic crystal fiber (PCF), demonstrating efficient power conversion between the HE11 and HE21 modes, with a maximum gain coefficient of 21.4 W−1 km−1. By exploring mechanical modes of different symmetries, we observe both polarization-dependent and polarization-independent intermodal Brillouin interaction. Finally, we discuss the role of squeeze film air damping and leakage mechanisms, ultimately critical to the engineering of PCF structures with enhanced interaction between high-order optical modes through flexural mechanical modes.

Investigation of a compact model for squeeze-film air damping in the free molecular regime

Due to the huge computational cost, the Monte Carlo (MC) model is difficult to use to predict squeeze-film air damping in the free molecular regime. Sumali (2007) proposed an empirical compact formula relating MC model and the analytical energy transfer model (ETM) by fitting two curves. By using the efficient numerical model, this paper discusses the application of the compact formula for squeeze-film air damping of different microplate sizes in the free molecular regime. The results show that, for plates of various sizes, the quality factors predicted by the compact model match well with those predicted by the numerical model. The work of this paper has validated that the compact model for squeeze-film air damping proposed by Sumali (2007) can be used for plates of various sizes.

Analytical model of squeeze film air damping of perforated plates in the free molecular regime

In this paper, an analytical model of squeeze film damping (SQFD) of perforated plates in the free molecular regime is developed, which is based on: (1) the modification of the perforated energy transfer model (P-ETM) (Li and Hu, J Micromech Microeng 21:025006, 2011) by giving the probability of molecules entering the gap through holes; (2) the application of Sumali’s formula (J Micromech Microeng 17:2231–2240, 2007) to relate to the Monte Carlo model (MC) (Hutcherson and Ye, J Micromech Microeng 14:1726–1733, 2004) quantitatively. The analytical model can model the perforation effect on SQFD of plates of various hole sizes. Compared with experiment data and numerical models, the analytical model is proved to be accurate, easy to operate. The effect of gap distance on SQFD of perforated plate in the free molecular regime is discussed. Due to perforation effect, as gap distance increases, the damping constant of non-perforated plate decreases faster than that of perforated plate of the same size.

An Efficient Numerical Model for Squeeze Film Air Damping of Microplates in the Free Molecular Regime

The squeeze film air damping of microplates in the free molecular regime has been received particular attention for many years. Based on Energy Transfer Model (ETM) proposed by Bao et al and Monte Carlo (MC) model proposed by Hutcherson and Ye, this paper proposes an efficient numerical model, compared with experiment data and present models, the present model costs less computational work than the previous MC model and is more accurate than ETM.

A generalized energy transfer model for squeeze-film air damping in the free molecular regime

A generalized energy transfer model (ETM) for squeeze-film air damping of micro plates in the free molecular regime is developed. The development of the model is based on: (1) the modification of the ETM proposed by Bao et al by using the weighted average of square traveling distance (l is the molecular traveling distance in the gap) to replace the plain average of , (2) the incorporation of the Monte Carlo (MC) model by Hutcherson and Ye so that some assumptions in Bao’s model causing the overestimation of quality factor are released, and (3) the use of Sumali’s empirical formula to relate the ETM to MC model quantitatively. The generalized ETM developed in this paper features: (1) a closed form equation for predicting quality factor according to the parameters of the system, (2) without suffering from the abnormal behavior when the aspect ratio of the plate goes high, and (3) good agreement with experimental results. As a result, the ETM can find practical applications in MEMS.

Performance of analysis crab leg based RF MEMS switch for defense and aerospace applications

In this paper the design and modeling of capacitive shunt switch for k-ka band applications is presented. The proposed model for this design is the crab leg flexure. In order to reduce the squeeze film air damping, the perforated switch with reduced spring constant is designed. Analysis of designed switch has been carried out on the various parameters of the switch such as damping factor, switching time, quality factor and Eigen frequencies in order to design a reliable switch. The results indicate that the obtained pull in voltage is 3.1V for the dielectric gap of 1mm and spring constant of 2.95N/m2. Switching time is observed as 1.2ms and 2.15ms for the gap of 1mm and 1.5mm respectively. The capacitance ratio i.e. Cdown/Cup is 211.11 for HfO2 and 100.741 for Si3N4. Resonant frequency is obtained as 14.45 KHz. Return loss is calculated as-44.85dB at a frequency of 1GHz and -25.68dB at a frequency of 27.5GHz and insertion loss is obtained as -0.0447db at 1GHz and -1.0379dB at 27.5GHz. The maximum peak isolation is observed as -59.5dB at 1GHz frequency and -71dB at 27.5GHz frequency.

Squeeze film air damping ratio analysis of a silicon capacitive micromechanical accelerometer

The dynamics behavior of most micro-electro-mechanical-system (MEMS) devices is significantly affected by the squeeze-film air damping. Therefore, the correct prediction of the squeeze-film air damping ratio is essential in MEMS devices design. In the paper, a static state test is proposed to measure the squeeze-film air damping ratios of a silicon capacitive micromechanical accelerometer under different pressures. The unsealed chip of capacitive accelerometer is placed in a vacuum extraction chamber and an open loop circuit is developed to apply step signal. By charging the pressure and measuring the overshoot M p and the settling time t s from the time response of the chip, the damping ratio ξ under different pressures can be calculated. Finite element method (FEM) based on the modified Reynolds equation is utilized to simulate the transient response of the micro-structure. Good correlation between experimental and numerical results is obtained. The proposed static state test in this paper provides a new and much easy method to measure the dynamic performances of micro-structures under various pressures.

Z-Axis Micromachined Tuning Fork Gyroscope with Low Air Damping

This paper reports on the design and fabrication of a z-axis tuning fork gyroscope which has a freestanding architecture. In order to improve the performance of the tuning fork gyroscope by eliminating the influence of the squeeze-film air 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 air damping in the gap between the proof masses and the substrate was eliminated. The proposed architecture was analyzed by the finite element method using ANSYS software. The simulated frequencies of the driving and sensing modes were 9.788 and 9.761 kHz, respectively. The gyroscope was fabricated using bulk micromachining technology. The quality factor and sensitivity of the gyroscope operating in atmospheric conditions were measured to be 111.2 and 11.56 mV/°/s, respectively.

Air damping models for micro- and nano-mechanical beam resonators in molecular-flow regime

Researches on energy dissipation of micro- and nano-mechanical beam resonators into the surrounding air are classified into two models, air drag force damping of the resonant beam vibrating in free space and squeeze film air damping of the resonant beam vibrating nearby walls. Appropriate application of these two models are crucial to the design of high-Q micro- and nano-mechanical beam resonators. In this paper, we will present a detail analysis on appropriate application range of these two models for evaluating air damping in micro- and nano-mechanical beam resonators. The two models are applied for investigating damping in the cantilevered and bridged beam resonators. The obtained analysis results show the significance difference between the two models for estimating the quality factor of the micro- and nano-mechanical beam resonators. The criterion for the distinction between the two models is derived by using the ratio factor of damping coefficients of micro- and nano-mechanical beam resonators.

The squeeze-film air damping of circular and elliptical micro-torsion mirrors

This paper proposes an analytical solution to calculate the squeeze-film air damping of circular and elliptical micro-torsion mirrors. To derive the expressions of squeeze-film air-damping torque, the nonlinear Reynolds equation, which governs the air behavior of torsion mirror, is solved by the method of eigenfunction expansions in polar coordinate and elliptical coordinate, respectively. The series solutions are integrated and summed up to deduce the damping torque of circular and elliptical torsion mirrors. The formulas of circular mirror and elliptical mirror are deduced independently, and their results match when the eccentricity of the elliptical mirror approaches zero. Besides, the results of the formulas are consistent with numerical simulation. Both of them verifies the damping torque formulas in this paper.

Design and finite element modeling of series-shunt configuration based RF MEMS switch for high isolation operation in K–Ka band

High isolation and low insertion loss is highly regarded for the devices designed for high frequency applications. A compact radio-frequency microelectromechanical systems switch on quartz substrate is presented in this paper. The high isolation is achieved by incorporating two membranes in series and shunt configuration on a single substrate while maintaining the compactness of the switch dimensions. The ohmic and capacitive switch membranes are designed in a cavity over co-planar waveguides on substrate. Spring constant, pull-in voltage, pressure distribution, squeeze film air damping, Q-factor, R, L and C for switch are calculated and analyzed by finite element modeler. Eigenfrequency analysis is also carried out using FEM to analyse the mode shape for first 6 eigenfrequencies. Biasing pads are provided on both ends of the switch for electrostatic actuation. Membranes with low spring constant are designed and optimized to work on same voltage level. Stress on membranes is analyzed and taken care of by the including meanders. This proposed switch is showing excellent isolation of $$75$$75 dB and low insertion loss of $$0.13$$0.13 dB at $$28$$28 GHz with need of actuation voltage of $$22.5$$22.5 V for both membranes in complete switch area of $$0.4$$0.4 mm$$^2$$2. The switch has wide bandwidth of $$30$$30 GHz from K and Ka band with above $$62$$62 dB of isolation.

Improving the Validity of Squeeze Film Air-Damping Model of MEMS Devices with Border Effect

Evaluation of squeezed film air damping is critical in the design and control of dynamic MEMS devices. The published squeezed film air damping models are generally derived from the analytical solutions of Reynolds equation or its other modified forms under the supposition of trivial pressure boundary conditions on the peripheral borders. These treatments ignoring the border effect can not give faithful result for structure with smaller air venting gap or the double-gimbaled structure in which the inner frame and outer one affect the air venting. In this paper, we use Green’s function to solve the nonlinear Reynolds equation with inhomogeneous boundary conditions. For two typical normal motion cases of parallel plate, the analytical models of squeeze film damping force with border effect are established. The viscous and inertial losses with real values and image values acoustic impedance are all included in the model. These models reduced the time consumption while giving satisfactory result. Without multifield coupling analysis, the estimation of the dynamic behavior of MEMS device is also allowed, and the simulation of the system performance is more convenient.

Numerical Studies of the Squeeze-Film Damping of MEMS Devices with Perforations in the Non-Continuum Regime

Predicting squeeze-film air damping of resonators in rare air is crucial in the design of high-Q devices for various applications. In the past, there have been two approaches to treat the squeeze-film air damping in non-continuum regime: using effective viscosity coefficient and using the molecular dynamics method. And most of the previous work focused on devices in which the rarefaction effects of air are not significant. For such cases, continuum theory is often adequate. However, we have investigated the air damping on oscillating structures in the free molecular regime in which classical continuum theory is no longer valid. Based on this premise, Hutcherson (2004 J. Micromesh. Microeng. 14 1726-1733) has developed a molecular dynamics simulation code and used in predicting quality factors of an oscillating micro-plate at low pressures. However, his work is valid only for non-perforated micro-plate. This paper, a brief description of the molecular dynamics method is presented first. Then a molecular dynamics simulation code has been developed and used in predicting quality factors of a perforated oscillating micro-plate in free molecular regime. And we have found that the molecular dynamics simulation results have shown an excellent agreement with the experimental data of Kwok et al. Finally, the limitations of the present molecular dynamics simulation code have been reported.

Study of a Novel MEMS Accelerometer with Low Noise Reduced by Actuators

A novel MEMS (Micro Electronic Mechanical System) capacitive accelerometer is presented, which is mainly composed of supporting beam, seismic mass, grid strip capacitances, comb capacitances and electrostatic driver. The damping of grid strip capacitances with variable overlapping area is mainly affected by the slide film air damping, which is small and neglectful, and the damping between comb capacitor is squeeze film air damping. The comb sensing gap can be reduced by electrostatic actuators by which the aspect ratio can reach to 75:1 which greatly depress the limitation of DRIE (Deep reactive ion etching) process on high aspect ratio, and the initial sensing capacitance increases from 2.97 pf to 14.87 pf. The squeeze film damping is reduced from 0.046 Nm/s to 0.0015 Nm/s by designing the comb-shaped grooves on the fixed comb electrodes. The comb initial sensing gap is optimized according to formation factors of system noise, and the noise is reduced from 1.395 μg/√HZ to 0.591 μg/√HZ. The simulation results show that the accelerometer sensitivity achieves 8.40 pf/g, which is two times of the conventional devices.

A dynamic collision model for improved over-range protection of cantilever-mass micromechanical accelerometers

A dynamic collision model is proposed and built to analyze over-range protection of cantilever beam–mass structured micro-accelerometers. The model encloses angular momentum of the seismic mass, squeeze-film air damping, inertial force and supporting force (acting at the cantilever-root) during the collision between the seismic mass and the over-range stopping bumpers. Based on angular momentum balance equation we obtain the relationship among the supporting force F, the collision time duration t and the rotation center c where the bumpers are located. In the best case of F=0 which means no supporting force acts on the cantilever, we find the optimal bumper location of c. The accelerometers have been fabricated with the over-range protection design according to the dynamic collision model. Experimental test shows that 5g measure-range accelerometers can endure 9000g acceleration and there is no sign of performance degradation, which well verified the dynamic collision model.

Damping mechanisms of single-clamped and prestressed double-clamped resonant polymer microbeams

In this article, an investigation of the damping mechanisms of resonant single- and double-clamped polymer microbeams for a frequency range from 10 kHz to 5 MHz is presented. The suspended structures are made of SU-8, an epoxy-type photoresist, by means of a sacrificial layer technique. The vibration was measured with a laser-Doppler vibrometer in high vacuum at different temperatures and at atmospheric pressure. The influence of air damping in rarefied air was investigated and the intrinsic damping mechanisms were determined in high vacuum (p<0.05 Pa). After excluding a variety of possible damping factors, the dominant intrinsic dissipation mechanism of the single-clamped microbeams was understood to be the material damping with maximum quality factors (Q) of around 70 at 20 °C. Quality factors of up to 720 at 20 °C were measured for stringlike double-clamped microbeams, which suggest a different intrinsic damping mechanism than material loss. It is shown that internal damping mechanisms due to flexure and elongation have a small impact on the damping of stretched strings. Modeling the clamping loss based on the wave transmission into the suspended anchor plates indicates that it is the dominant intrinsic dissipation in the prestressed double-clamped microresonators. At atmospheric pressure it was shown that at low frequencies the quality factors of single-clamped and stringlike double-clamped microbeams are limited by the squeeze-film air damping. At high frequencies the quality factors are limited by the specific intrinsic damping. In between the two particular regions with a specific dominant damping mechanism the quality factors show a maximum.