Measurement of the Young’s modulus using micro-cantilevered beam actuated by electrostatic force

Abstract

Determining the Young’s modulus accurately is important in micro-electro-mechanical systems (MEMS) design. Generally, the Young’s modulus of a micro-component is measured by the resonance method, of which the actuation is electrostatic force. However, this method does not take the effect of the electrostatic force on the resonant frequency into consideration. Thus, the test error becomes more obvious as the DC voltage increases. In this paper, an improved resonance method, determining the Young’s modulus of a micro-cantilever beam, is proposed, which takes the nonlinearity of the electrostatic force into consideration. This method has three obvious advantages: only one simple micro-cantilevered beam sample is needed; it is unnecessary to find the initial thickness of the gas film between the beam and the substrate; the accuracy of the measurement result of the Young’s modulus is improved. In order to obtain the resonant frequency of a cantilevered beam actuated by a DC voltage, the dynamic equations of the micro-cantilevered beam in multi-field coupled situations are established, and the effect of the electrostatic force on the resonant frequency of the micro-beam is investigated. Results show that, the Young’s modulus can be found by measuring the resonant frequency and DC voltage. The dynamics performances of the micro-structure are influenced by the nonlinearity of the electrostatic force, and the electrostatic effect should be observed especially when the beam becomes smaller, through general studies. Finally, the experimental principle of measuring the Young’s modulus is designed and conducted to verify these theories. The Young’s modulus of brass is measured exactly.