Analysis of Mechanical Vibrations of Membranes of Capacitive Type Micromechanical Switches

Capacitance control of capacitive type micromechanical switches occurs at a high frequency due to a change of the distance between the flexible membrane and the reference electrode. Membrane oscillation will affect the electrical signals and operational characteristics of such switches. The aim of the work was to determine the values of vibrations of thin membranes under high-frequency exposure and compare them with the values of static bending under a similar constant force. The finite element analysis method was used with the recalculation of grid positions using the Euler–Lagrange method, with further modal and harmonic analysis of membrane vibrations under the action of a periodically varying ponderomotor force calculated for the selected voltage range. Gold and tungsten were considered as membrane materials. For considered membrane geometry the oscillation amplitude of the gold membrane in the studied preresonance frequency range is 16–21 % higher than the static bending value, whereas for the tungsten membrane it is only 2.2–3.2 %, which is explained by the significantly higher modulus of elasticity of tungsten. A more rigid membrane is also characterized by high values of natural frequencies. An increasing in the amplitude of the ponderomotor force leads to a multiple increasing of membrane vibration amplitudes, but does not change the shape of the amplitude-frequency response. The relevance of studying membrane vibrations in the preresonance values is shown. Constructive ways of increasing the rigidity of membranes and optimizing the design of MEMS systems with oscillation elements are given.

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