Iteration scheme for the solution of the two-dimensional Schro¨dinger-Poisson equations in quantum structures
作者:
A. Trellakis,
A. T. Galick,
A. Pacelli,
U. Ravaioli,
期刊:
Journal of Applied Physics
(AIP Available online 1997)
卷期:
Volume 81,
issue 12
页码: 7880-7884
ISSN:0021-8979
年代: 1997
DOI:10.1063/1.365396
出版商: AIP
数据来源: AIP
摘要:
A fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schro¨dinger’s and Poisson’s equations is presented. Using quantum mechanical perturbation theory, a simple expression describing the dependence of the quantum electron density on the electrostatic potential is derived. This expression is then used to implement an iteration scheme, based on a predictor-corrector type approach, for the solution of the coupled system of differential equations. We find that this iteration approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the approach 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, the convergence is six times faster by applying our predictor-corrector approach compared to a corresponding underrelaxation algorithm. ©1997 American Institute of Physics.
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