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Excitons in nanocrystals: Ab initio calculations
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Image of FIG. 1.
FIG. 1.

Nanocrystal atomic configuration for different molar fractions. The atomic species H, Si, and Ge are represented in white, yellow, and green, respectively. Their respective LUMO and HOMO orbitals integrated in the coordinate are also shown.

Image of FIG. 2.
FIG. 2.

Average bond lengths (in angstroms) for different molar fractions of a NC 1.4 nm in diameter.

Image of FIG. 3.
FIG. 3.

Molar fraction dependence of the quasiparticle (, solid diamonds) and HOMO-LUMO (, solid circles) gaps and the self-energy interation (, solid squares). For the sake of comparison, the LDA results of Melnikov et al. are displayed with open symbols (Ref. 19). The GW-corrected HOMO-LUMO gaps of Yu et al. are represented by crosses (Ref. 39).

Image of FIG. 4.
FIG. 4.

Molar fraction -dependence of the exciton energy for NCs 1.4 nm in diameter with (solid circles) and without (solid squares) the contribution of . For comparison, we also display PEM energies (open and solid stars, Ref. 38), the scaled PL data of Takeoka et al. (solid diamonds, Refs. 6 and 17), and the GW-corrected HOMO-LUMO gaps of Yu et al. (crosses, Ref. 39).

Image of FIG. 5.
FIG. 5.

(a) Molar fraction dependence of the exciton binding energy of the NCs 1.4 nm in diameter. The inset shows the exciton exchange energy (solid diamonds), as compared with those by Weissker et al. (open diamonds, Ref. 24) and Reboredo et al. (cross diamonds, Ref. 29). (b) Molar fraction dependence of the wave function dispersion of the LUMO (solid circles) and HOMO (open circles) orbitals.

Image of FIG. 6.
FIG. 6.

The molar fraction -dependence of the radiative recombination lifetime of NCs 1.4 nm in diameter (solid squares). All values are normalized with respect to the case where . For comparison, we also display the normalized radiative lifetimes of Takeoka et al.(Ref. 17, solid diamonds), Weissker et al. (Ref. 38, open and solid stars), and Yu et al. (crosses, Ref. 39).


Generic image for table
Table I.

Detailed atomic compositions and bond structures for all molar fractions cases investigated in this work. The NC diameter is approximately equal to 1.4 nm.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Excitons in Si1−xGex nanocrystals: Ab initio calculations