Electronic and optical fine structure of GaAs nanocrystals: the role of d orbitals in a tight-binding approach

Electronic structure and optical spectra of GaAs nanocrystals for a wide range of sizes are studied by using both $sp^3s^*$ and $sp^3s^*d^5$ nearest-neighbor tight-binding models. Our results show that the inclusion of $d$ orbitals into a minimal basis set is necessary for a proper description of the lowest electron states, especially in the strong confinement regime. For dot sizes below 2.5 nm, the ground electron state is primarily built of L-point bulk band-states, giving the nanocrystals indirect-gap character. Simpler $sp^3s^*$ models yield an incorrect description of electron states made from bulk band- states away from the Brillouin zone center. In contrast, $sp^3s^*d^5$ models are able to provide a consistent picture of the main optical features in agreement with experiments.