@article{959e0ce64e284b6884e6c6e58d7bc622,
title = "Comparison of iteration schemes for the solution of the multidimensional Schr{\"o}dinger-Poisson equations",
abstract = "We present a fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schr{\"o}dinger's and Poisson's equations in quantum structures. A simple expression describing the dependence of the quantum electron density on the electrostatic potential is used to implement a predictor- corrector type iteration scheme for the solution of the coupled system of differential equations. This approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the algorithm by presenting an example for the calculation of the two-dimensional bound electron states within the cross-section of a GaAs-AlGaAs based quantum wire. For this example, six times fewer iterations are needed when our predictor-corrector approach is applied, compared to a corresponding underrelaxation algorithm.",
keywords = "Iteration, Predictor-corrector, Quantum wire, Schr{\"o}dinger-Poisson, Semiconductor, Simulation",
author = "A. Trellakis and Galick, {A. T.} and A. Pacelli and U. Ravaioli",
note = "Funding Information: Trellakis A. trell@ceg.uiuc.edu 1 Galick A. T. 1 Pacelli A. 2 Ravaioli U. 1 1 Beckman Institute University of Illinois at Urbana-Champaign Urbana, IL 61801 USA uillinois.edu 2 Dipartimento di Elettronica e Informazione and CEQSE-CNR Politecnico di Milano Piazza Leonardo da Vinci 32 Milano 20133 Italy polimi.it 1998 8 1-4 105 109 1998 Copyright {\textcopyright} 1998 Hindawi Publishing Corporation We present a fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schr{\"o}dinger's and Poisson's equations in quantum structures. A simple expression describing the dependence of the quantum electron density on the electrostatic potential is used to implement a predictor – corrector type iteration scheme for the solution of the coupled system of differential equations. This approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the algorithm by presenting an example for the calculation ofthe two-dimensional bound electron states within the cross-section of a GaAs-AlGaAs based quantum wire. For this example, six times fewer iterations are needed when our predictor – corrector approach is applied, compared to a corresponding underrelaxation algorithm. Semiconductor simulation quantum wire iteration predictor-corrector Schr{\"o}dinger- Poisson http://dx.doi.org/10.13039/100000001 National Science Foundation ECS 95-09751 http://dx.doi.org/10.13039/100000001 National Science Foundation ECD 89-43166 ",
year = "1998",
doi = "10.1155/1998/42712",
language = "English (US)",
volume = "8",
pages = "105--109",
journal = "VLSI Design",
issn = "1065-514X",
publisher = "Hindawi Publishing Corporation",
number = "1-4",
}