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.

Investigation of a complete squeeze-film damping model for MEMS devices

Dynamic performance has long been critical for micro-electro-mechanical system (MEMS) devices and is significantly affected by damping. Different structural vibration conditions lead to different damping effects, including border and amplitude effects, which represent the effect of gas flowing around a complicated boundary of a moving plate and the effect of a large vibration amplitude, respectively. Conventional models still lack a complete understanding of damping and cannot offer a reasonably good estimate of the damping coefficient for a case with both effects. Expensive efforts have been undertaken to consider these two effects, yet a complete model has remained elusive. This paper investigates the dynamic performance of vibrated structures via theoretical and numerical methods simultaneously, establishing a complete model in consideration of both effects in which the analytical expression is given, and demonstrates a deviation of at least threefold lower than current studies by simulation and experimental results. This complete model is proven to successfully characterize the squeeze-film damping and dynamic performance of oscillators under comprehensive conditions. Moreover, a series of simulation models with different dimensions and vibration statuses are introduced to obtain a quick-calculating factor of the damping coefficient, thus offering a previously unattainable damping design guide for MEMS devices.

Thermo-viscous acoustic modeling of perforated micro-electro-mechanical systems (MEMS)

An analytical model based on the low reduced-frequency method is developed for the damping and spring force coefficients of micro-electro-mechanical systems (MEMS) structures. The model is based on a full-plate approach that includes thermal and viscous losses and hole end effects, as well as inertial and compressibility effects. Explicit analytical formulas are derived for damping and spring forces of perforated circular MEMS with open and closed edge boundary conditions. A thermo-viscous finite-element method (FEM) model is also developed for the numerical solution of the problem. Results for the damping and spring coefficients from the analytical models are in good agreement with the FEM results over a large range of frequencies and parameters. The analytic formulas obtained for the damping and spring coefficients provide a useful tool for the design and optimization of perforated MEMS. Specifically, it is shown that for a fixed perforation ratio of the back-plate the radius of the holes can be optimized to minimize the damping.

Wide Bandwidth and Low Driving Voltage Vented CMUTs for Airborne Applications

This paper presents a novel method to increase the bandwidth (BW) of airborne capacitive micromachined ultrasonic transducers (CMUTs). This method introduces a gaseous squeeze film as a damping mechanism, which induces a stiffening effect that lowers the pull-in voltage and improves the sensitivity. The optimal behavior of this stiffening effect versus the damping mechanism can be controlled by creating optimized fluidic trenches of various heights within the gap. The fractional BW can be controlled from 0.89% to 8.1% by adjusting the trench height while lowering the pull-in voltage to less than 54 V at the gap height of 1.0 [Formula: see text]. To achieve the largest sensitivity and lowest pull-in voltage at a given BW, we have developed a multi-parameter optimization method to adjust all combinations of design parameters. A novel multiple hard-mask process flow has been developed to enable fabrication of CMUTs with different cavity and trench heights on the same wafer. These devices provided an equivalent noise pressure level of 4.77 μ Pa/ √ Hz with 6.24-kHz BW for 7.6- [Formula: see text] deep fluidic trenches and 4.88 μ Pa/ √ Hz with 7.48-kHz BW for 14.3- [Formula: see text] deep fluidic trenches. This demonstration of the wide-BW CMUTs with high sensitivity and low pull-in voltage makes them applicable to medical and thermoacoustic imaging, nondestructive testing, and ultrasonic flow metering.

Squeeze Film Air Damping in Tapping Mode Atomic Force Microscopy

In dynamic plowing lithography, the sample surface is indented using a vibrating tip in tapping mode atomic force microscopy. During writing, the gap between the cantilever and the sample surface is very small, usually on the order of micrometers. High vibration frequency and small distance induce squeeze film air damping from the air in the gap. This damping can cause variations in the cantilever's vibrating parameters and affect the accuracy of the nanoscale patterning depth. In this paper, squeeze film air damping was modeled and analyzed considering the inclined angle between the cantilever and the sample surface, and its effects on the resonant amplitude and damping coefficient of the cantilever were discussed. The squeeze film air damping in the approaching curve of cantilever was observed, and its effect on fabricating nanopatterns was discussed.