Corrected squeezed-film damping simulation validated with a lorentz-force magnetometer operating in vacuum

A number of corrections to the well-known squeezed-film gas damping model are required to get accurate results for MEMS. This paper reports on the implementation and validation of a corrected squeezed-film damping (SFD) simulation for common MEMS structures, electrostatic comb fingers, under various vacuum levels. Experimental Q factors were measured for the first in-plane resonant mode of a Lorentz-force magnetometer. An acoustic boundary condition was implemented to accommodate, in different areas of the sensor, various ratios a/h of squeezing surface characteristic dimension a to squeezed gas gap h. At a typical operating pressure for this sensor, e.g. 10Pa, corresponding to Knudsen number Kn ∼ 670, the simulated Q factor is within +/-25% of the measured value. This new, corrected simulation approach provides, for the first time, a practical and accurate way of predicting Q factors for complex capacitive MEMS sensors such as accelerometers, gyroscopes and magnetometers that operate at low pressure.