A NEW METHODOLOGY FOR 2-DIMENSIONAL NUMERICAL-SIMULATION OF SEMICONDUCTOR-DEVICES

Abstract

A new 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's equation and a surface mapping technique is developed to treat arbitrary surface boundary conditions. As a result of the proposed new solution method, the two-dimensional potential distribution can 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 with a new algorithm to get the self-consistent solution of full set of semiconductor device equations without any outer iteration. Comparisons between the proposed method and the Gummel's method in Si-MESFET simulation are made. It is demonstrated that the convergent rate of the proposed method can be speeded up to 4-8 times over the Gummel's method. The proposed new iterative method can be incorporated with the conventional solution method such as the Gummel's method to get a stable and efficient computation scheme for device simulation.