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

Abstract

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.