A new methodology for two-dimensional numerical simulation of semiconductor devices

A methodology for obtaining the self-consistent solution of semiconductor device equations discretized in the finite-difference scheme is proposed, in which a new discretized Green´s function solution method is used to solve the two-dimensional discretized Poisson equation and a surface mapping technique is developed to treat arbitrary surface boundary conditions. The two-dimensional potential distribution can then be expressed in terms of charge density distribution and bias conditions. Using the derived potential distribution, the SLOR-nonlinear iteration for the current continuity equations of both carriers can be performed by incorporating a new algorithm to obtain the self-consistent solution of a full set of semiconductor device equations without any outer iteration. An Si MESFET simulation demonstrates that the convergent rate of the proposed method can be speeded up to 4-8 times that of Gummel´s method. The new method can be incorporated with the conventional solution methods to get a stable and efficient computation scheme