Nonlinear Dynamics

, Volume 88, Issue 4, pp 2817–2829 | Cite as

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

Original Paper

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.

Keywords

Group preserving scheme Poisson–Boltzmann equation Reproducing kernel method Lie symmetry analysis 

Mathematics Subject Classification

15A60 

Notes

Compliance with ethical standards

Conflict of interests

The authors declare that they do not have any competing or conflict of interests.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Art and Science FacultySiirt UniversitySiirtTurkey
  2. 2.Department of Mathematics, Science FacultyFırat UniversityElazığTurkey
  3. 3.Department of Mathematics, Basic Science FacultyUniversity of BonabBonabIran

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