We analyze the electronic structure of group III-V semiconductors obtained within full potential linearized augmented plane wave (FP-LAPW) method and arrive at a realistic and minimal tight-binding model, parametrized to provide an accurate description of both valence and conduction bands. It is shown that the cation $s{p}^3$- anion $s{p}^3{d}^5$ basis along with the next nearest neighbor model for hopping interactions is sufficient to describe the electronic structure of these systems over a wide energy range, obviating the use of any fictitious $s^{*}$ orbital, employed previously. Similar analyses were also performed for the II-VI semiconductors, using the more accurate FP-LAPW method compared to previous approaches, in order to enhance reliability of the parameter values. Using these parameters, we calculate the electronic structure of III-V and II-VI nanocrystals in real space with sizes ranging up to about $7\mathrm{nm}$ in diameter, establishing a quantitatively accurate description of the bandgap variation with sizes for the various nanocrystals by comparing with available experimental results from the literature.

• Received 13 January 2005

DOI:https://doi.org/10.1103/PhysRevB.72.045333