Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

Li, Yiming; Voskoboynikov,; Lee, C. P.; Sze, Simon M.; Tretyak, O. V.

doi:10.1140/epjb/e2002-00250-6

Cited by 9 publications

(10 citation statements)

References 1 publication

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“…Problems of this type have been computationally treated by Li, Voskoboynikov, Lee, Liu, Sze and Tretyak in [9], [10], [17] using the so called Full Approximation Method, where each eigenvalue is targeted separately and where each iteration step requires the solution of a linear eigenproblem. Hence, for reasonably fine discretizations S (λ)x = 0 this method is much too expensive.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…It can be further transformed into a form where the spin dependence only dwells in the boundary conditions [6], [14] resulting in two Schrödinger equations which differ only on the interface conditions between the quantum dot and the surrounding bulk material. Numerical experiments demonstrating the influence of the spin-orbit splitting on the relevant energy levels for rotationally symmetric quantum dots are contained in [9], [10], [15], [16], [17], where the Schrödinger equations are discretized by finite differences, and the resulting nonlinear eigenproblem is solved by the full approximation method.…”

Section: Introductionmentioning

confidence: 99%

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Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting

Betcke

Voß

2007

Appl Math

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In this work we derive a pair of nonlinear eigenvalue problems corresponding to the one-band effective Hamiltonian accounting for the spin-orbit interaction governing the electronic states of a quantum dot. We show that the pair of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions which are satisfied for our example of a cylindrical quantum dot and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise an efficient iterative projection method simultaneously handling the pair of nonlinear problems and thereby saving about 25 % of the computation time as compared to the Nonlinear Arnoldi method applied to each of the problems separately.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting

Betcke

Voß

2007

Appl Math

View full text Add to dashboard Cite

show abstract

“…In 2001, Yiming Li et al, [6] used Computer simulation of electron energy levels for different shape ⁄ semiconductor quantum dots. In 2002, Yiming Li et al, [7] used Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots. In 2003, Melnik et al, [4] applied finite element analysis of Nanowire superlattice structures.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Method Linear Triangular Element for Solving Nanoscale InAs⁄GaAs Quantum Ring Structures

Hussain

Al-Hawasy

Ali

2019

MJS

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This paper concerned with the solution of the nanoscale structures consisting of the with an effective mass envelope function theory, the electronic states of the quantum ring are studied. In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of quantum rings are studied by the one electronic band Hamiltonian effective mass approximation, the energy- and position-dependent on electron effective mass approximation, and the spin-dependent on the Ben Daniel-Duke boundary conditions. In the description of the Hamiltonian matrix elements, the Finite elements method with different base linear triangular element is adopted. The non-linear energy confinement problem is solved approximately by using the Finite elements method with linear triangular element, to calculate the energy of the electron states for the quantum ring.

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“…In 2001,Yiming Li et al, [1] usedComputer simulation of electron energy levels for different shape ⁄ semiconductor quantum dots. In 2002,Yiming Li et al, [2] used Electron energy state spin-splitting in 3D cylindricalsemiconductor quantum dots. In 2003,Melnik et al, [5]applied finite element analysis of Nanowire superlattice structures.Whereas2005,Yiming Li, [6] using an iterative method for single and vertically stacked semiconductor quantum dots simulation.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Method withPiecewise Linear Function for Solving NanoscaleInAs⁄GaAsQuantum RingStructures

Hussain

Al-Hawasy

Ali

2019

ANJS

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In this paper concerned with the solution of the nanoscale structures consisting of the ⁄ with an effective mass envelope function theory, the electronic states of the ⁄ quantum ring are studied.In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of ⁄ quantum rings are studied by the one electronic band Hamiltonian effective mass approximation, the energy-and position-dependent on electron effective mass approximation, and the spin-dependent on the Ben Daniel-Duke boundary conditions. In the description of the Hamiltonian matrix elements, the Finite elements method with different base piecewise linear function is adopted. The non-linear energy confinement problem is solved approximately by using the Finite elements method with piecewise linear function, to calculate the energy of the one electron states for the ⁄ quantum ring. The results of numerical example are compared for accuracy and efficiency with the finite element method of linear triangular element. This comparison shows that good results of numerical example.

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Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

Cited by 9 publications

References 1 publication

Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting

Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting

Finite Element Method Linear Triangular Element for Solving Nanoscale InAs⁄GaAs Quantum Ring Structures

Finite Element Method withPiecewise Linear Function for Solving NanoscaleInAs⁄GaAsQuantum RingStructures

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