Effects of dielectric confinement and electron-hole exchange interaction on excitonic states in semiconductor quantum dots

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Abstract

A general scheme is established within the effective-mass approximation to calculate systematically the excitonic energy spectra in a semiconductor quantum dot including the dielectric confinement effect. This effect is found to appear most pronounced in the quantum-dot structure in comparison with the quantum-well and quantum-wire structures. A formula of the lowest exciton energy in the strong confinement regime is derived and the significance of the dielectric confinement effect is clarified. We investigate the dependence of the binding energy and the oscillator strength of the lowest-energy excitonic state on the quantum-dot radius, the electron-to-hole mass ratio, and the dielectric-constant ratio between the quantum dot and the surrounding medium. The subband mixing effect due to the electron-hole Coulomb interaction gives a finite oscillator strength to excitonic transitions which are forbidden in the absence of the Coulomb interaction. This effect is shown unambiguously in the calculated excitonic energy spectra. Furthermore, the electron-hole exchange interaction in a quantum dot is discussed. The short-range part of the exchange energy is shown to increase in proportion to the inverse of the volume of the quantum dot as the quantum-dot size is reduced. On the other hand, the long-range part of the exchange energy is found to be sensitively dependent on the shape of the quantum dot. In particular, it vanishes for the optically allowed excitonic states in a spherical quantum dot.

Original languageEnglish
Pages (from-to)4569-4584
Number of pages16
JournalPhysical Review B
Volume47
Issue number8
DOIs
Publication statusPublished - 1993
Externally publishedYes

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Exchange interactions
Semiconductor quantum dots
quantum dots
Electrons
interactions
Coulomb interactions
oscillator strengths
energy spectra
energy transfer
Semiconductor quantum wires
quantum wires
Binding energy
Excitons
mass ratios
Electron energy levels
Semiconductor quantum wells
proportion
Permittivity
binding energy
excitons

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

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abstract = "A general scheme is established within the effective-mass approximation to calculate systematically the excitonic energy spectra in a semiconductor quantum dot including the dielectric confinement effect. This effect is found to appear most pronounced in the quantum-dot structure in comparison with the quantum-well and quantum-wire structures. A formula of the lowest exciton energy in the strong confinement regime is derived and the significance of the dielectric confinement effect is clarified. We investigate the dependence of the binding energy and the oscillator strength of the lowest-energy excitonic state on the quantum-dot radius, the electron-to-hole mass ratio, and the dielectric-constant ratio between the quantum dot and the surrounding medium. The subband mixing effect due to the electron-hole Coulomb interaction gives a finite oscillator strength to excitonic transitions which are forbidden in the absence of the Coulomb interaction. This effect is shown unambiguously in the calculated excitonic energy spectra. Furthermore, the electron-hole exchange interaction in a quantum dot is discussed. The short-range part of the exchange energy is shown to increase in proportion to the inverse of the volume of the quantum dot as the quantum-dot size is reduced. On the other hand, the long-range part of the exchange energy is found to be sensitively dependent on the shape of the quantum dot. In particular, it vanishes for the optically allowed excitonic states in a spherical quantum dot.",
author = "Toshihide Takagahara",
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AB - A general scheme is established within the effective-mass approximation to calculate systematically the excitonic energy spectra in a semiconductor quantum dot including the dielectric confinement effect. This effect is found to appear most pronounced in the quantum-dot structure in comparison with the quantum-well and quantum-wire structures. A formula of the lowest exciton energy in the strong confinement regime is derived and the significance of the dielectric confinement effect is clarified. We investigate the dependence of the binding energy and the oscillator strength of the lowest-energy excitonic state on the quantum-dot radius, the electron-to-hole mass ratio, and the dielectric-constant ratio between the quantum dot and the surrounding medium. The subband mixing effect due to the electron-hole Coulomb interaction gives a finite oscillator strength to excitonic transitions which are forbidden in the absence of the Coulomb interaction. This effect is shown unambiguously in the calculated excitonic energy spectra. Furthermore, the electron-hole exchange interaction in a quantum dot is discussed. The short-range part of the exchange energy is shown to increase in proportion to the inverse of the volume of the quantum dot as the quantum-dot size is reduced. On the other hand, the long-range part of the exchange energy is found to be sensitively dependent on the shape of the quantum dot. In particular, it vanishes for the optically allowed excitonic states in a spherical quantum dot.

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