Pull-in voltage study of electrostatically actuated fixed-fixed beams using a VLSI on-chip interconnect capacitance model

A highly accurate computationally efficient closed-form model has been developed to determine the pull-in voltage of an electrostatically actuated fixed-fixed beam. The approach includes the electrostatic spring softening effects due to the fringing field capacitances along with the nonlinear spring hardening effects associated with the load-deflection characteristics of a uniformly loaded fixed-fixed beam. Meijs and Fokkema´s highly accurate empirical formula for the capacitance of a VLSI on-chip interconnect has been used to determine the spring softening effects due to the fringing field capacitances. The developed model has been verified by comparing the results with published experimentally verified three-dimensional (3-D) finite element analysis (FEA) results and with those from other published representative closed-form models. The developed model can determine the pull-in voltage with a maximum deviation of 1.27% from the FEA results for small deflections and for large deflections (airgap-beam thickness ratio =12), the deviation from the FEA results is 2.0%. A maximum deviation of 0.5% from the FEA results has been observed for extreme fringing field cases (beamwidth-airgap ratio ≤0.5). The model´s accuracy range is better compared to the other published models.