High Quality Factor Resonant MEMS Accelerometer With Continuous Thermal Compensation

Abstract

We report a new silicon MEMS accelerometer based on differential Frequency Modulation (FM) with experimentally demonstrated thermal compensation over a dynamic temperature environment and µg-level Allan deviation of bias. The sensor architecture is based on resonant frequency tracking in a vacuum packaged SOI tuning fork oscillator. To address drift over temperature, the MEMS sensor die incorporates two identical tuning forks with opposing axes of sensitivity. Demodulation of the differential FM output from the two simultaneously operated oscillators eliminates common mode errors and provides an FM output with continuous thermal compensation. The first SOI prototype with quality factor of 350,000 was built and characterized over a temperature range between 30 • C and 75 • C. Temperature characterization of the FM accelerometer showed less than a 0.5 % scale-factor change throughout a temperature range from 30 • C to 75 • C, without any external compensation. This is enabled by an inherently differential frequency output, which cancels common-mode influences, such as those due to temperature. Allan deviation of the differential FM accelerometer revealed a bias instability of 6 µg at 20 s, along with an elimination of any temperature drift due to increases in averaging time. After comparing the measured bias instability with the designed linear range of 20 g, the sensor demonstrates a wide dynamic range of 130 dB. A second design iteration of the FM accelerometer, vacuum-sealed with getter material, was created to maximize Q-factor, and thereby frequency resolution. A Q-factor of 2.4 million was experimentally demonstrated, with a time constant of greater than 20 minutes. have achieved this level of performance for targeting and inertial applications, through the use of temperature post-compensation algorithms. A few examples include Northrop Grumman Corporation's NGC (USA) SiAc [1], Colibrys' (Switzerland) RS9010 [2], [3], Georgia Institute of Technology (USA) [4], University of Southampton, (UK) [5], and Institute for Nanostructures (Portugal), Univ. of the British Columbia (Canada), Delft University of Technology (The Netherlands) [6]. Conventional micromachined pendulous accelerometers rely on Amplitude Modulation (AM) of the input stimulus, where the inertial input produces a proportional change in the sensor output voltage. In other words, the inertial input is amplitude modulated. In this approach, the final output signal of the sensor is proportional to the true input, as well as a number of device parameters, including the stiffness of the springs, pick-up electronics gain, and so on. These additional factors contribute to the bias and scale factor of the sensor and require calibration to eliminate their influence. Variation of these internal parameters with time and environment also produce unpredictable drifts in the sensor output, and as such, these analogue devices typically show poor long term and environmental stability. These types of accelerometers are typically limited in terms of in-run bias stab...

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