Efficient Poisson equation solvers for large scale 3D simulations

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Self-consistent semiconductor device modeling requires repeated solution of the 2D or 3D Poisson equation that describes the potential profile in the device for a given charge distribution. As a result, efficient methods for the solution of 2D and 3D Poisson's equations are desired. The preconditioned bi-conjugate gradient stabilized (BiCGSTAB) method has demonstrated efficient, albeit nonmonotonic, convergence properties. It has also been shown that for a large number of points in the spatial domain, multi-grid techniques offer enhanced performance over other iterative solvers due to their multi-mode reduction of error and the fact that the codes can be easily implemented on parallel computers. In this paper, a particular combination of these methods, the multi-grid preconditioned BiCGSTAB method, is explored. Varying results on the number of grids and the level of over-relaxation of the smoothers reveal the underlying strength of the combined scheme. The convergence properties of the developed solver are tested on a variety of device structures, including a 3D pn-junction diode and a split-gate silicon on insulator (SOI) device, schematically shown in Fig. 1. This later device structure is currently being fabricated within the Nanostructures Research Group at Arizona State University. The 3D Poisson equation solver is also used in examining the role of the top and bottom depletion gates on the inversion layer electron density in the channel region of the SOI device from Fig. 1.

Original languageEnglish (US)
Title of host publication2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001
EditorsM. Laudon, B. Romanowicz
Pages23-26
Number of pages4
StatePublished - Dec 1 2001
Event2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001 - Hilton Head Island, SC, United States
Duration: Mar 19 2001Mar 21 2001

Publication series

Name2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001

Other

Other2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001
CountryUnited States
CityHilton Head Island, SC
Period3/19/013/21/01

ASJC Scopus subject areas

  • Engineering(all)

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    Speyer, G., Vasileska, D., & Goodnick, S. (2001). Efficient Poisson equation solvers for large scale 3D simulations. In M. Laudon, & B. Romanowicz (Eds.), 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001 (pp. 23-26). (2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001).