Electron-hole correlations in semiconductor quantum dots with tight-binding wave functions

The electron-hole states of semiconductor quantum dots are investigated within the framework of empirical tight-binding descriptions for Si, as an example of an indirect-gap material, and InAs and CdSe as examples of typical III-V and II-VI direct-gap materials. We significantly improve the energies of the single-particle states by optimizing tight-binding parameters to give the best effective masses. As a result, the calculated excitonic gaps agree within 5% error with recent photoluminescence data for Si and CdSe but they agree less well for InAs. The electron-hole Coulomb interaction is insensitive to different ways of optimizing the tight-binding parameters. However, it is sensitive to the choice of atomic orbitals; this sensitivity decreases with increasing dot size. Quantitatively, tight-binding treatments of Coulomb interactions are reliable for dots with radii larger than 15–20 Å . Further, the effective range of the electron-hole exchange interaction is investigated in detail. In quantum dots of the direct-gap materials InAs and CdSe, the exchange interaction can be long ranged, extending over the whole dot when there is no local ~onsite! orthogonality between the electron and hole wave functions. By contrast, for Si quantum dots the extra phase factor due to the indirect gap effectively limits the range to about 15 Å, independent of the dot size.