A new analytical method for modeling a 2D electrostatic potential in MOS devices, applicable to compact modeling

Abstract

This paper presents a new conformal mapping method to solve 2D Laplace and Poisson equations in MOS devices. More specifically, it consists of an analytical solution of the 2D Laplace equation in a rectangular domain with Dirichlet boundary conditions, with arbitrary values on the boundaries. The advantages of the new method are that all four edges of the rectangle are taken into account and the solution consists of closed-form analytical expressions, which make it fast and suitable for compact modeling. The new model was validated against other similar methods. It was found that the new model is much faster, easier to implement, and avoids many numerical issues, especially near the boundaries, at the cost of a very small loss in accuracy.