Research On The Performance Of Force-Balanced Micro-Accelerometer With Errors In The Support Beams

Force-balanced micro-accelerometer, based on electrostatic driving and sensing technology, has many advantageous attributes, such as good linearity, wide dynamic range, high sensitivity, and strong reliability. Due to the faulty of micromachining, there always exist errors between the actual parameters and that designed, for instances, the size error of support beams, the gap error of comb fingers and the center offset of proof-mass. The errors in support beams certainly cause the bending rigidity of the support beams asymmetry and lead to the proof-mass to translate in the direction of electrostatic force and turn round as well. This two-degree-of-freedom compound motion of the proof-mass surely has some effects on the performance of a force-balanced micro-accelerometer. This thesis will focus on this new issue.The main work and conclusions of this thesis are as followings:(1) Three common used structures of MEMS (MicroElectroMechanical System), i.e. parallel capacitor system with two-end fixed beam, micro-accelerometer with two-end fixed beam and micro-accelerometer with double folded beams, are token as the examples to analyze the deflection of supporting beams with errors under the applied forces. The formulas corresponding to the resistances to the applied force for the three structures, named equivalent stiffness, are derived. It is shown that the resistances to the applied force for all the three structures are in a same manner of two-dimensional equivalent stiffness while the only difference lies in the formula to calculate the elements of equivalent stiffness matrix. The equivalent stiffness is necessary for the analysis of electromechanical coupling characteristics of electrostatic MEMS.(2) There is a strong relationship between the performance of electrostatic MEMS and its electromechanical coupling characteristics. For the purpose to investigate the influence of errors in support beams on electromechanical coupling characteristics, electromechanical coupling macro models with two degrees of freedom for both single parallel capacitor system and double parallel capacitor system are established respectively, and the performances of these two systems are analyzed. This thesis analyzes the effect of electrostatic stiffness, and the electrostatic stiffness matrix is derived. The static response of the system is analyzed, the static pull-in voltage is obtained by the method of optimization, and it is verified by finite element simulation. In addition to these, the dynamic response of the system is also analyzed provided the damping in the system is ignored. It is shown that the motion of system will vary with the changing of the input voltage. Employing the method of optimization, the dynamic pull-in voltage for this system is also obtained. Along the same line, static response of the double parallel capacitor system is analyzed, and the static pull-in voltage is obtained. All the work above lays down the foundation for the analysis of performances of force-balanced micro-accelerometer.(3) Applying the methods proposed in this thesis and the results concerned with the electromechanical coupling characteristics as the parallel capacitor system undergoing the two-degree-of-freedom compound motion, an electromechanical coupling model with two degrees of freedom for force-balanced micro-accelerometer is established. The influences caused by the errors in the support beams on the performances of the micro-accelerometer, including sensitivity, nonlinear errors, zero bias, are analyzed. The results show that the errors in the support beams will affect the sensitivity and nonlinearity errors of the micro-accelerometer, but the affection may be reduced by increasing the gain of feedback voltage, even when the gain of the feedback is large enough, the influence can be completely neglected. The external perturbing force, such as thermal residual stress, has no effects on the sensitivity of the accelerometer. But it will cause bias and additional nonlinear errors, and no matter what the gain of feedback is, the zero bias and nonlinear errors cannot be reduced.