### 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 language | English |
---|---|

Pages (from-to) | 4569-4584 |

Number of pages | 16 |

Journal | Physical Review B |

Volume | 47 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1993 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

**Effects of dielectric confinement and electron-hole exchange interaction on excitonic states in semiconductor quantum dots.** / Takagahara, Toshihide.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Effects of dielectric confinement and electron-hole exchange interaction on excitonic states in semiconductor quantum dots

AU - Takagahara, Toshihide

PY - 1993

Y1 - 1993

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=24544445905&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24544445905&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.47.4569

DO - 10.1103/PhysRevB.47.4569

M3 - Article

AN - SCOPUS:24544445905

VL - 47

SP - 4569

EP - 4584

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 8

ER -