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2012 | 1 | 58-79
Tytuł artykułu

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

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
1
Strony
58-79
Opis fizyczny
Daty
otrzymano
2012-09-05
poprawiono
2012-10-15
zaakceptowano
2012-10-15
online
2012-11-16
Twórcy
  • Department of Applied Mathematics, National Hsinchu University of
    Education, Hsinchu 300, Taiwan
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