MEMS capacitive accelerometer: dynamic sensitivity analysis based on analytical squeeze film damping and mechanical thermoelasticity approaches

Abstract

In this work, we adopt a semi-analytical model to study a capacitive MEMS accelerometer based in silicon (Si). Such model takes into account the thermoelastic stiffness and linear expansion coefficients of anisotropic bulk Si. In addition, an analytical damping model, derived from the Reynolds equation, is incorporated in the model, in order to study dynamical characteristics of a MEMS capacitive accelerometer. Such approach takes into account the inertial effects on squeeze film damping in air, argon and helium gases, assumed as being ideal gases. The simulation model was compared with experimental measurements. The main figure of merit adopted is the electromechanical sensitivity (SEM), assuming frequency response and considering the effect of gas pressure, as well as temperature, on the damping loss mechanisms in such devices. The resulted model implementation shows a good agreement with the experimental data. For all gases, the sensitivity at 20 Pa presents less variation than at 200 Pa. At 20 Pa, the linear response of the device reaches up to 300 Hz, approximately, for air and helium, assuming variation of ≈ 0.5 dB, no matter which temperature. For 200 Pa, the linear response drops down to about 150 Hz. Also, for the three gases, the variation of SEM as a function of temperature is below 0.17 dB in the entire operational range, for both evaluated pressures, depending only on the silicon mechanical properties at low frequencies.