chapter  4
48 Pages


As semiconductor technology continues to evolve, numerical modelling of the electrical behaviour of advanced devices has become vital. Numerical device modelling based on the self-consistent solution of the fundamental semiconductor equations dates back to the famous work of Gummel in 1964 [1]. In Gummel’s one-dimensional (1D) discretization, the Poisson equation and the current continuity equations are decoupled and solved sequentially until convergence. Gummel’s approach was later extended by de Mari [2] and applied to transient simulations of a 1D p-n junction. A very important breakthrough in the discretization of the current transport equations was reported by Scharfetter and Gummel in 1969 [3]. The Scharfetter-Gummel (SG) discretization scheme has since been used by all important device simulation programs.