关键词: 边缘场效应, 尺度效应, 阶梯型悬臂梁, 偶应力理论, 吸合电压

Abstract: Aiming at the stepped micro-cantilever beam commonly used in electrostatically actuated micro electromechanical systems (MEMS) devices, a pull-in voltage calculation method is proposed. Based on a modified couple stress theory and Euler theory, the pull-in voltage model is derived by the energy method. The beam deflection is expressed as the product of a trial function and an unknown coefficient, and the solving process is simplified by using Taylor's expansion. The proposed method is validated by comparing with the finite element solutions. Further the selection of trial function and the determination of the Taylor's expansion order are discussed, the pull-in behaviour of stepped beam is investigated, and the comparison with the traditional method is made. The results show that the truncation error can be neglected as setting the Taylor's expansion order to be 8. The prediction error of the proposed model is less than 5% when using its deflection function, and the predicted results are obviously superior to the traditional method. The pull-in voltage monotonously increase with the increase of width ratio, and first decrease and then increase with the increase of length ratio, which can provide information for the design of low actuation voltage of MEMS devices. The proposed model considers the effect of the fringing field and the size-dependence, and can be used to predict the pull-in voltage in micro/nano scale.

Key words: couple stress theory, fringing field, pull-in voltage, size-dependence, stepped cantilever