Efficient Poisson Equation Solvers for Large Scale 3D Simulations

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Self-consistent semiconductor device modeling requires repeated solution of the 2D or 3D Poisson equation that describes the potential profile of the device for a given charge distribution. As a result, efficient methods for the solution of 2D and 3D Poisson 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 impleented on parallel computers. In this paper, a particular combination of these methods, the multi-gride 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 in a variety of device structures, including a 3D pn-junction doide and a split-gate silicon on insulator (SOI) device. 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 later electron density in the channel region of the SOI device.

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Journal: TechConnect Briefs
Volume: 1, Technical Proceedings of the 2001 International Conference on Modeling and Simulation of Microsystems
Published: March 19, 2001
Pages: 23 - 26
Industry sector: Sensors, MEMS, Electronics
Topics: Modeling & Simulation of Microsystems
ISBN: 0-9708275-0-4