Equivalent Electrical Circuit Model of MEMS Resonator

Evaluation of the quality of packaging used in microelectromechanical devices is a non-trivial task. A method for calculating the parameters of a low-frequency microelectromechanical resonator that will be used as a vacuum gauge for assessing the quality of packaging technology is proposed in this paper. The proposed method uses a combination of finite-element analysis implemented using COMSOL, simulation of equivalent electrical circuits of microelectromechanical resonators using SPICE, and calculation by analytical models. The applied models allow to estimate the range of output currents at a given value of input voltages and characteristic parameters of the geometry of the resonator structure, due to the required values of the resonant frequency of the device and technological limitations. The dependences of the output currents on the input voltages and the size of the gaps between the movable beams of the resonator and the electrodes are obtained. According to estimates, the value of the output currents is from 10 nA to 10 μA in the studied ranges of input voltages for an electrostatic transduction gap width of 2 μm. The results can be used to design connection circuits for the resonator, such as a circuit for a transimpedance amplifier of the output resonator signal, so that the vacuum parameters in the package can be studied.