Exact analytical solution to the Poisson-Boltzmann equation for semiconductor devices

Elyas Shivanian; Saeid Abbasbandy; Mohammed S. Alhuthali

doi:10.1140/epjp/i2014-14104-5

EPJ

Exact analytical solution to the Poisson-Boltzmann equation for semiconductor devices

Elyas Shivanian¹, Saeid Abbasbandy¹^* and Mohammed S. Alhuthali²

¹ 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

Received: 9 December 2013
Accepted: 23 April 2014
Published online: 2 June 2014

Abstract

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.