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.

A Unified Channel Charges Expression for Analytic MOSFET Modeling

“…The gate voltage Vg relative to flat band is [5,14] a noniterative expression of the surface potential which serves as a reference for surface potential-based models. In the following, we generated u S (y) by first-order Taylor expansion as previously done in [6]. u S (y) versus Vg at a constant drain bias V (y) is generated by…”

“…Equation (26) was previously calculated in a large range of drain and gate voltages and presented in [6]. (17) gives a simplified drain current expression in a single integral:…”

“…The Pao-Sah double integral gives an expression of the transconductance from the derivative, g = dI D /dV g in (26) [6]: A simplified expression of the transconductance can be obtained from (27) by a derivative under the integral using db(Vg)/dV g from (20) as follows:…”

“…New approaches of MOSFET surface potential modeling were performed from analytic treatment and have brought a renewal in analytic resolution of surface potential [2][3][4][5]. We previously used a similar method in the analytic description of surface potential by Taylor expansion [6].…”

Modeling and Simulation of Special Shaped SOI Materials for the Nanodevices Implementation

“…The modeling of the classical devices [1] or novel nanodevices [2] improves the design and explains some phenomena experimentally encountered [3].…”