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Active and Passive Electronic Components
Volume 2010, Article ID 268431, 11 pages
Research Article

Taylor Expansion of Surface Potential in MOSFET: Application to Pao-Sah Integral

1LaMIPS, Laboratoire commun NXP-CRISMAT, UMR 6508 CNRS ENSICAEN, UCBN, 2, rue de la Girafe BP 5120, F-14079 Caen Cedex 5, France
2NXP Semiconductors 2, Esplanade Anton Philips Campus Effiscience, Colombelles, BP 20 000 14906 Caen Cedex 9, France

Received 16 October 2009; Revised 24 March 2010; Accepted 21 April 2010

Academic Editor: Ashok Goel

Copyright © 2010 Hugues Murray et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a simple model, derived from Pao-Sah theory, valid in all modes from weak to strong inversion, to calculate the drain current in Metal Oxide Semiconductor Field Effect Transistor (MOSFET). The Pao-Sah double integral is decomposed into single integrals with limits of integration calculated from Taylor polynomials of inverse functions. The solution is presented analytically wherever possible, and the integration is made from simple numerical methods (Simpson, Romberg) or adaptative algorithms and can be implemented in simple C-program or in usual mathematical software. The transconductance and the diffusion current are also calculated with the same model.