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VLSI Design
Volume 8 (1998), Issue 1-4, Pages 545-548

A 3D Nonlinear Poisson Solver

Department of Electromagnetic Theory, Budapest Technical University, Budapest 1521, Hungary

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Poisson equation is solved in a rectangular prism of semiconductor with the boundary conditions commonly used in semiconductor device modeling. There is a planar heterojunction inside the prism. The finite difference formulation leading to a matrix of seven diagonals is used. The 3D version of the Stone's method is applied for the iterative solution of the matrix equation. The nonlinear dependence of the carrier concentration on the electrostatic potential is taken into account. The heterojunction is modeled by a potential jump. The advantages and limits of the method is presented.