A new analytical method of solving 2D Poisson's equation in MOS devices applied to threshold voltage and subthreshold modeling

Abstract

In this paper we present a new theoretical approach in MOS modeling to derive analytical, physics-based model equations for the geometry and voltage dependence of threshold voltage and for the subthreshold behavior of short-channel MOSFETs. Our approach uses conformal mapping techniques to analytically solve the two-dimensional Poisson equation, whereby inhomogeneous substrate doping is taken into account. The presented model consists of analytical equations in closed form and uses only physically meaningful parameters. Therefore, the results are not only useful in circuit simulators but also in calculations of scaling behavior, where planned processes can be investigated. Comparison with numerical device simulation results and measurements confirm the high accuracy of the presented model.