Generalized closed form approximations for pull-in characteristics of electrostatic nanotweezers under the influences of van der waals and casimir forces

This paper presents generalized closed form expressions for predicting the accurate pull-in characteristics of nanotweezers. The coupled electromechanical problem of electrostatic nanotweezers is formulated with Galerkin´s approximation considering the effects of intermolecular forces and fringe field. The resulting integrals and higher order polynomials are solved numerically to determine the closed form expressions for critical pull-in values. The derived results are compared and validated quantitatively with reported literature showing reasonable agreement. It has been further shown that the incorporation of the intermolecular forces and fringe effect leads to significant reduction in pull-in voltage. As the derived expressions do not involve any complex mathematical operation unlike in reported literature, it can be easily used by designers for quick yet accurate estimation of critical pull-in parameters.