The Performance Effects of Squeeze Film Stiffness on Non-resonate Interferometric Inertial Sensors

This paper studies the nonlinear effects of squeeze film stiffening on the performance of a high resolution MEMS nonresonant inertial sensor. It is shown that these effects introduce a surprising dynamic response that extends the operational frequency range of the devices by retarding the resonate response. In addition, this performance advantage will occur without the traditional gain trade-off associated with linear systems of this type. A method is introduced to experimentally characterize the squeeze film stiffness of a passive inertial sensor through the resonant characterization of a Fabry-Pérot interferometric accelerometer under reduced pressure. Such passive devices are uniquely suited for the study of squeeze films and, due to the dependence of both the sensitivity and bandwidth on the device structural stiffness, variation of the stiffness with frequency must be considered to accurately predict sensor performance. The characterization confirms established analytical squeeze film stiffness theory in the continuous gas regime for conditions of Knudsen numbers less then one. As the Knudsen number equal to one is approached, it is shown that ideal kinetic gas theory and continuous squeeze film theory converge yielding a simplified stiffness estimate at resonance under reduced pressure. These analytical results are used to predict the performance gains due to the nonlinear, frequency dependent total stiffness of the sensor during non-resonant operation. ∗Address all correspondence to this author. INTRODUCTION The characterization of structural parameters is central to the design and performance analysis of inertial sensors employing proof-mass elements. In many Microelectromechanical System (MEMS) devices, the stiffness due to a squeeze film may be a significant component of the total suspension stiffness of such an element. However, in contrast to the stiffness due to flexural suspension members, the squeeze film stiffness is nonlinear and may introduce some surprising dynamic effects. Squeeze films are formed between closely vibrating surfaces due to the dynamic encapsulation of viscous gases, a representation of such is shown in Figure 1. The earliest description was by Crandell in 1918 [1] for circular plates in parallel motion and a more complete derivation was presented by Langlois in 1962 [2]. Squeeze film effects are commonly encountered in MEMS sensors and actuators due to the small dimensions and the frequent reliance on vibratory motion, such as in micromachined accelerometers [3] and mirrors [4, 5]. For example, squeeze film damping is commonly examined in relation to the quality factor of the amplitude response of resonant devices, as in [6]. Less frequently examined is the effect of squeeze film stiffening on non-resonant sensors. Most prominently, Andrews et. al considered the experimental effects of both the damping and stiffness of a squeeze film formed between the square plates of a vibrating microstructure on it’s frequency response [7]. The mechanical sensitivity, resolution and usable frequency range (bandwidth) of many non-resonant sensors (such as the 1 Copyright c © 2007 by ASME