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-Pe´rot 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 under the resonant response 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.