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Group preserving scheme and reproducing kernel method for the Poisson–Boltzmann equation for semiconductor devices

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Abstract

This paper introduces that the nonlinear Poisson–Boltzmann equation for semiconductor devices describing potential distribution in a double-gate metal oxide semiconductor field effect transistor (DG-MOSFET) is exactly solvable. The DG-MOSFET shows one of the most advanced device structures in semiconductor technology and is a primary focus of modeling efforts in the semiconductor industry. Lie symmetry properties of this model is investigated in order to extract some exact solutions. The reproducing kernel Hilbert space method and group preserving scheme also have been applied to the nonlinear equation. Numerical results show that the present methods are very effective.

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Notes

  1. \(\mathcal {A}\) is an element of the Lie algebra so(2, 1) of the proper orthochronous Lorentz group \(SO_0(2, 1)\).

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Authors and Affiliations

  1. Department of Mathematics, Art and Science Faculty, Siirt University, 56100, Siirt, Turkey

    Ali Akgül

  2. Department of Mathematics, Science Faculty, Fırat University, 23119, Elazığ, Turkey

    Mustafa Inc

  3. Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, 55517-61167, Iran

    Mir Sajjad Hashemi

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  1. Ali Akgül
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Correspondence to Ali Akgül.

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Akgül, A., Inc, M. & Hashemi, M.S. Group preserving scheme and reproducing kernel method for the Poisson–Boltzmann equation for semiconductor devices. Nonlinear Dyn 88, 2817–2829 (2017). https://doi.org/10.1007/s11071-017-3414-4

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