Abstract
We present a fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrödinger'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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 105-109 |
| Number of pages | 5 |
| Journal | VLSI Design |
| Volume | 8 |
| Issue number | 1-4 |
| DOIs | |
| State | Published - Jan 1 1998 |
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Keywords
- Iteration
- Predictor-corrector
- Quantum wire
- Schrödinger-Poisson
- Semiconductor
- Simulation
ASJC Scopus subject areas
- Hardware and Architecture
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
Cite this
Comparison of iteration schemes for the solution of the multidimensional Schrödinger-Poisson equations. / Trellakis, A.; Galick, A. T.; Pacelli, A.; Ravaioli, Umberto.
In: VLSI Design, Vol. 8, No. 1-4, 01.01.1998, p. 105-109.Research output: Contribution to journal › Review article
}
TY - JOUR
T1 - Comparison of iteration schemes for the solution of the multidimensional Schrödinger-Poisson equations
AU - Trellakis, A.
AU - Galick, A. T.
AU - Pacelli, A.
AU - Ravaioli, Umberto
PY - 1998/1/1
Y1 - 1998/1/1
N2 - We present a fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrödinger'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.
AB - We present a fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrödinger'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.
KW - Iteration
KW - Predictor-corrector
KW - Quantum wire
KW - Schrödinger-Poisson
KW - Semiconductor
KW - Simulation
UR - http://www.scopus.com/inward/record.url?scp=0032309272&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032309272&partnerID=8YFLogxK
U2 - 10.1155/1998/42712
DO - 10.1155/1998/42712
M3 - Review article
AN - SCOPUS:0032309272
VL - 8
SP - 105
EP - 109
JO - VLSI Design
JF - VLSI Design
SN - 1065-514X
IS - 1-4
ER -