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Analytical solutions of cubic and quintic polynomials in micro and nanoelectronics using the Lambert-Tsallis Wq function

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Abstract

There are many problems in nanoelectronics whose solutions are roots of cubic or quintic polynomials. In most of these cases, the analytical solutions are not known and numerical methods are used. In this direction, the present work shows the analytical solutions of the roots of some cubic and quintic functions, as well they are used to provide the analytical solutions for the pull in point of a simple microactuator, for the space charge limited current in a nanowire and for the displacement of a plate due to the Casimir force in a nanoelectromechanical device. The analytical solutions are simple to handle and they permit a better understanding of the role of the physical parameters.

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Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001, and CNPq via Grant No. 307184/2018-8.

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  1. Laboratory of Quantum Information Technology, Department of Teleinformatic Engineering, Federal University of Ceara - DETI/UFC, Campus do Pici, C.P. 6007, Fortaleza, CE, 60455-970, Brazil

    R. V. Ramos

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Ramos, R.V. Analytical solutions of cubic and quintic polynomials in micro and nanoelectronics using the Lambert-Tsallis Wq function. J Comput Electron 21, 396–400 (2022). https://doi.org/10.1007/s10825-022-01852-6

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