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

A new methodology for obtaining the self-consis­ tent solution of semiconductor device equations discretized in the finite-difference scheme is proposed, in which a new discre­ lized Green's function solution method is used to solve the two­ dimensional discretized Poisson's equation and a surface map­ ping 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 itera­ tion for the current continuity equations of botb carriers can be performed by incorporating with a new algorithm to get the self-consistent solution of full set of semiconductor device equa­ tions 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 computa­ tion scheme for device simulation.