Tight-binding model for semiconductor nanostructures

An empirical ${s}_{c}{p}_{a}^{3}$ tight-binding (TB) model is applied to the investigation of electronic states in semiconductor quantum dots. A basis set of three $p$ orbitals at the anions and one $s$ orbital at the cations is chosen. Matrix elements up to the second nearest neighbors and the spin-orbit coupling are included in our TB model. The parametrization is chosen so that the effective masses, the spin-orbit splitting and the gap energy of the bulk CdSe and ZnSe are reproduced. Within this reduced ${s}_{c}{p}_{a}^{3}$ TB basis the valence $(p)$ bands are excellently reproduced and the conduction $(s)$ band is well reproduced close to the $\ensuremath{\Gamma}$ point, i.e., near to the band gap. In terms of this model much larger systems can be described than within a (more realistic) $s{p}^{3}{s}^{*}$ basis. The quantum dot is modeled by using the (bulk) TB parameters for the particular material at those sites occupied by atoms of this material. Within this TB model we study pyramidal-shaped CdSe quantum dots embedded in a ZnSe matrix and free spherical CdSe quantum dots (nanocrystals). Strain effects are included by using an appropriate model strain field. Within the TB model, the strain effects can be artificially switched off to investigate the influence of strain on the bound electronic states and, in particular, their spatial orientation. The theoretical results for spherical nanocrystals are compared with data from tunneling spectroscopy and optical experiments. Furthermore the influence of the spin-orbit coupling is investigated.