Exact analytical solution to the Poisson-Boltzmann equation for semiconductor devices
Department of Mathematics, Imam Khomeini International University, 34149-16818, Ghazvin, Iran
2 Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589, Jeddah, Saudi Arabia
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Accepted: 23 April 2014
Published online: 2 June 2014
This paper shows 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 represents one of the most advanced device structures in semiconductor technology and is a primary focus of modeling efforts in the semiconductor industry. Furthermore, exact analytical solution is obtained in the implicit form for further physical interpretation and a full discussion is given.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2014