Deflection and Pull-In of a Misaligned Comb Drive Finger in an Electrostatic Field

Abstract

The elastic deflection of a comb drive finger in an electrostatic field is considered. The finger can be symmetrically located between two rigid fingers of the matching comb, in which case the problem reduces to a pure bifurcation problem for which the critical voltage can be determined. Alternatively, due to the nonlinear motion of an approximate straight-line guidance mechanism, the base of the finger can have a lateral and angular displacement, which results in a smooth curve of equilibria with a limit point, after which pull-in occurs. An analytic model is derived, which is validated by 2-D and 3-D finite-element analyses and experiments. For the analytic model, an assumed deflection shape and a series expansion of the electrostatic capacity yield the deflection curves. This shows that the pull-in occurs at a voltage that is reduced by an amount that is about proportional to the two-third power of the relative base displacement. The theoretical results for the case of a lateral base displacement have been experimentally tested. The results show a qualitative agreement with the analytic model, but the experimental deflections are larger and the pull-in voltages are lower. The finiteelement analyses show that these differences can be explained from neglected fringe fields and deviations from the nominal shape.[2013-0270]

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“…In this equation E is the Young's modulus of silicon, which has a minimum value of 130 GPa [22], ϵ 0 is the vacuum permittivity of 8.85 × 10 −12 F m −1 , and VPI is the normalized pull-in voltage of 3.516 [24]. For comb fingers with a length l of 120 µm and a thickness t of 3 µm the maximum voltage to be applied is 164 V. Meijaard et al [25] show that for misaligned fingers due to quasi straight-line flexures the limit point voltage decreases with 22% for lateral deflections up to 200 nm. The number of fingers in the comb-drives is chosen such that the required actuation voltage is always below a safe value of 80 V. Flexure pull-in occurs when the lateral mechanical stiffness of the complete flexure mechanism is insufficient to withstand the negative 'electrostatic stiffness' as a result of the electric field.…”

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“…Meijaard et al [89] show that for misaligned fingers due to quasi straight-line flexures the limit point voltage decreases with 22 % for lateral deflections up to 200 nm. The number of fingers in the comb-drives is chosen such that the required actuation voltage is always below a safe value of 80 V.…”