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Volumn 64, Issue 12, 2001, Pages

Shape effects on the one- and two-electron ground state in ellipsoidal quantum dots

Author keywords

[No Author keywords available]

Indexed keywords

PHOSMET;

EID: 0035883405     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.125325     Document Type: Article
Times cited : (71)

References (68)
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    • and references therein
    • A D. Yoffe, Adv. Phys.50, 1 (2001) and references therein.
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  • 52
    • 85038935284 scopus 로고    scopus 로고
    • About the validity of this infinite barrier model, let us note that it has been shown, for example, for CdSe nanocrystals (Refs., and, that in the framework of the Kane model (Ref. it is possible to analytically take into account the finite barrier height at the dot boundary and the nonparabolicity of the conduction band (valence- and conduction-band mixing). It comes out that for either quantum wells deep enough or large quantum dots the electron envelop wave function is null at the boundary, as in the parabolic single-band model we are using. Moreover, a self-consistent equation is derived, which gives the corrections to the confined electrons energy levels with respect to the simple effective-mass model, due to the conduction-band nonparabolicity. These corrections are size dependent. If we use this equation for a spherical quantum dot with radius (formula presented), we find that the single-electron ground-state energy varies at most a few meV. Because here we want to study two-electron correlations effects which become significant only for large dots, we can conclude that the single-band, effective-mass model should not fail for our purposes
    • About the validity of this infinite barrier model, let us note that it has been shown, for example, for CdSe nanocrystals (Refs. 53 and 54), that in the framework of the Kane model (Ref. 55) it is possible to analytically take into account the finite barrier height at the dot boundary and the nonparabolicity of the conduction band (valence- and conduction-band mixing). It comes out that for either quantum wells deep enough or large quantum dots the electron envelop wave function is null at the boundary, as in the parabolic single-band model we are using. Moreover, a self-consistent equation is derived, which gives the corrections to the confined electrons energy levels with respect to the simple effective-mass model, due to the conduction-band nonparabolicity. These corrections are size dependent. If we use this equation for a spherical quantum dot with radius (formula presented), we find that the single-electron ground-state energy varies at most a few meV. Because here we want to study two-electron correlations effects which become significant only for large dots, we can conclude that the single-band, effective-mass model should not fail for our purposes.
  • 67
    • 85038921683 scopus 로고    scopus 로고
    • We must point out that the exact formal solution can be written as a series expansion (Ref. whose coefficients are solutions of suitable recurrence equations. These equations cannot be solved analytically. This means that solutions can be obtained only by using numerical methods, but their accuracy can be controlled. In our case convergence up to 0.01% on the eigenvalues has been achieved
    • We must point out that the exact formal solution can be written as a series expansion (Ref. 44), whose coefficients are solutions of suitable recurrence equations. These equations cannot be solved analytically. This means that solutions can be obtained only by using numerical methods, but their accuracy can be controlled. In our case convergence up to 0.01% on the eigenvalues has been achieved.
  • 68
    • 85038905687 scopus 로고    scopus 로고
    • The strong confinement regime is defined by the condition that the typical dot dimensions be much less than the electron Bohr radius (formula presented) (Ref. For example, for CdSe we have (formula presented) and we must require that (formula presented)
    • The strong confinement regime is defined by the condition that the typical dot dimensions be much less than the electron Bohr radius (formula presented) (Ref. 8). For example, for CdSe we have (formula presented) and we must require that (formula presented)


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.