1993
DOI: 10.1063/1.354921
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Self-consistent simulation of quantum wires in periodic heterojunction structures

Abstract: We simulate the low temperature confinement of electrons in quantum wires formed at the corners of periodic saw-tooth structures consisting of layers of AlxGa1−xAs and GaAs materials. A very efficient self-consistent procedure for the solution of Schrödinger’s and Poisson’s equations, including shifted periodic boundary conditions, is used to obtain the wave functions and energy levels in the quantum well. Self-consistency is very important to obtain an accurate result; in particular, the precise details of th… Show more

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Cited by 23 publications
(9 citation statements)
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“…In the last two decades, several computer-simulation programs have been written with the aim of finding the potential and mobile charge density distribution in conventional devices [2][3][4][5][6], Ravailoli et al [7] and Kerkhoven et al [8,9] have reported self-consistent computations of the electronic states of a quantum wire while Kumar et al [10][11][12] have presented self-consistent numerical solutions of the Poisson and Schrödinger equations for a GaAs-Al x Ga 1−x As quantum dot. Kerkhoven et al [8,9] work is for two-dimensional (2D) devices.…”
Section: Introductionmentioning
confidence: 98%
See 1 more Smart Citation
“…In the last two decades, several computer-simulation programs have been written with the aim of finding the potential and mobile charge density distribution in conventional devices [2][3][4][5][6], Ravailoli et al [7] and Kerkhoven et al [8,9] have reported self-consistent computations of the electronic states of a quantum wire while Kumar et al [10][11][12] have presented self-consistent numerical solutions of the Poisson and Schrödinger equations for a GaAs-Al x Ga 1−x As quantum dot. Kerkhoven et al [8,9] work is for two-dimensional (2D) devices.…”
Section: Introductionmentioning
confidence: 98%
“…Kerkhoven et al [8,9] work is for two-dimensional (2D) devices. Kumar et al [11], working in three dimensions (3D), use a Newton loop for the Poisson equation with a polynomial preconditioned conjugate gradient method or the Lanczos method for the solution of the Hermitian matrix system.…”
Section: Introductionmentioning
confidence: 99%
“…This procedure must be repeated until convergence is reached. Due to the strong nonlinear coupling between both equations, a straightforward iteration by itself does not guarantee convergence, and more sophisticated approaches must be employed [40][41][42].…”
Section: Numerical Strategymentioning
confidence: 99%
“…The one-dimensional electron distribution, nSID, may be calculated by solving the twodimensional Poisson's (1) and Shrodinger's (7) equations self-consistently [6,7],…”
Section: A 1-d Electron Gasmentioning
confidence: 99%