Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation

Jinn-Liang Liu

Nanoscale Systems: Mathematical Modeling, Theory and Applications (2012)

  • Volume: 1, page 58-79
  • ISSN: 2299-3290

Abstract

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Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock version are then presented for calculating the wanted eigenvalues that are clustered in the interior of the spectrum and may have small gaps and degeneracy. These are challenging issues arising from modeling a great variety of semiconductor nanostructures fabricated by advanced technology in semiconductor industry and science. Generic algorithms for many-electron simulations under this framework are also provided. Numerical results obtained within this framework are summarized to three eminent aspects, namely, accuracy of models, physical novelty, and effectivity of nonlinear eigensolvers. Concerning numerical accuracy, important details related to experimental data are also addressed.

How to cite

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Jinn-Liang Liu. "Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation." Nanoscale Systems: Mathematical Modeling, Theory and Applications 1 (2012): 58-79. <http://eudml.org/doc/267280>.

@article{Jinn2012,
abstract = {Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock version are then presented for calculating the wanted eigenvalues that are clustered in the interior of the spectrum and may have small gaps and degeneracy. These are challenging issues arising from modeling a great variety of semiconductor nanostructures fabricated by advanced technology in semiconductor industry and science. Generic algorithms for many-electron simulations under this framework are also provided. Numerical results obtained within this framework are summarized to three eminent aspects, namely, accuracy of models, physical novelty, and effectivity of nonlinear eigensolvers. Concerning numerical accuracy, important details related to experimental data are also addressed.},
author = {Jinn-Liang Liu},
journal = {Nanoscale Systems: Mathematical Modeling, Theory and Applications},
keywords = {Quantum dots; electronic structure; quantum models; nonlinear eigenproblems; Jacobi-Davidson method; quantum dots},
language = {eng},
pages = {58-79},
title = {Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation},
url = {http://eudml.org/doc/267280},
volume = {1},
year = {2012},
}

TY - JOUR
AU - Jinn-Liang Liu
TI - Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation
JO - Nanoscale Systems: Mathematical Modeling, Theory and Applications
PY - 2012
VL - 1
SP - 58
EP - 79
AB - Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock version are then presented for calculating the wanted eigenvalues that are clustered in the interior of the spectrum and may have small gaps and degeneracy. These are challenging issues arising from modeling a great variety of semiconductor nanostructures fabricated by advanced technology in semiconductor industry and science. Generic algorithms for many-electron simulations under this framework are also provided. Numerical results obtained within this framework are summarized to three eminent aspects, namely, accuracy of models, physical novelty, and effectivity of nonlinear eigensolvers. Concerning numerical accuracy, important details related to experimental data are also addressed.
LA - eng
KW - Quantum dots; electronic structure; quantum models; nonlinear eigenproblems; Jacobi-Davidson method; quantum dots
UR - http://eudml.org/doc/267280
ER -

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