Generalized closed form approximations for pull-in characteristics of fixed-fixed nano beam under the influences of van der Waals and Casimir forces

• Autores: Banibrata Mukherjee, Siddhartha Sen
• Localización: Microelectronics reliability, ISSN 0026-2714, Nº. 94, 2019, págs. 32-40
• Idioma: inglés
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• Resumen

  • In this paper, we have presented generalized closed form solutions to estimate the permissible dimensional limits for the basic design parameters as well as the accurate pull-in characteristics of electrostatically actuated fixed-fixed nano beam. The coupled electromechanical problem for the nano beam is formulated using Galerkin's approximation while considering the effects of fringe field, mid-plane stretching and intermolecular forces like van der Waals and Casimir. The resulting integrals and higher order polynomials are solved numerically to determine the closed form expressions for allowable detachment length, minimum feasible gap, and critical pull-in parameters. The derived expressions are compared quantitatively with other reported results which show reasonable agreement. The advantage here is that the derived expressions do not involve any complex mathematical operation unlike in existing literature, and thus the expressions can be readily used for quick and accurate estimation of the design parameters. As the applied voltage exceeds beyond pull-in limit, it can lead to severe structural failure during operation; hence the designers must be aware of the accurate pull-in expressions as derived in this paper. It has been observed that the incorporation of the intermolecular forces together with the fringe effect leads to significant reduction in pull-in voltage whereas the mid-plane stretching parameter shows the opposite effect. It is further envisaged that, the proposed generalized closed form expressions will serve as quick guidelines for reliable and safe design and fabrication of various similar electrostatically actuated nanosystems.