Open Access

ARTICLE

Efficient Numerical Solution of the 3-D Semiconductor Poisson Equation for Monte Carlo Device Simulation

by Z. Aksamija¹, U. Ravaioli³

1 Corresponding Author: aksamija@illinois.edu.
2 Electrical and Computer Engineering, University of Illinois at Urbana/Champaign .
3 Beckman Institute for Advanced Science and Technology and University of Illinois at Urbana/Champaign.

Computer Modeling in Engineering & Sciences 2008, 37(1), 45-64. https://doi.org/10.3970/cmes.2008.037.045

Abstract

Finding the scalar potential from the Poisson equation is a common, yet challenging problem in semiconductor modeling. One of the central problems in traditional mesh-based methods is the assignment of charge to the regular mesh imposed for the discretisation. In order to avoid this problem, we create a mesh-free algorithm which starts by assigning each mesh point to each particle present in the problem. This algorithm is based on a Fourier series expansion coupled with point matching. An efficient algorithm for repeatedly solving the Poisson problem for moving charge distributions is presented. We demonstate that this approach is accurate and capable of solving the Poisson equation on any point distribution.

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Keywords

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