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

• Autorzy: Jinn-Liang Liu
• 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.

Słowa kluczowe

EN

Quantum dots; electronic structure; quantum models; nonlinear eigenproblems; Jacobi-Davidson method

Kategorie tematyczne

• 65N06: Finite difference methods
• 65F15: Eigenvalues, eigenvectors

• 73.23.Hk: Coulomb blockade; single-electron tunneling
• 78.67.Hc: Quantum dots
• 73.21.La: Quantum dots

• Wydawca: De Gruyter Open
• Czasopismo: Nanoscale Systems: Mathematical Modeling, Theory and Applications
• Rocznik: 2012
• Tom: 1
• Strony: 58-79

Daty

otrzymano

2012-09-05

poprawiono

2012-10-15

zaakceptowano

2012-10-15

online

2012-11-16

Twórcy

autor

Jinn-Liang Liu

• Department of Applied Mathematics, National Hsinchu University of
  Education, Hsinchu 300, Taiwan

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Identyfikatory

DOI

10.2478/nsmmt-2012-0005