Semiconductor nanocrystals and embedded quantum dots: Electronic and optical properties

A tight-binding model for semiconductor quantum dots (QD) consisting of a small gap semiconductor material A embedded within a larger gap material B is used to determine the bound, localized one-particle QD-states. The form and symmetry properties of these states and their dependence on form, size and composition of the QDs are discussed. The Coulomb and dipóle matrix elements between these states are calculated so that a many-body Hamiltonian is derived describing the elctronic properties of the QDs and the coupling to an applied (optical) electric field. Truncating the many-particle Hubert space by taking into account only a finite number of localized electron and hole states the many-body Hamiltonian can be solved exactly. The resulting excitation spectrum and optical properties are presented and discussed. The method is, in particular, applied to CdSe QDs embedded in ZnSe with zincblende structure, to CdSe nanocrystals, and to InN QDs embedded in GaN with wurtzite structure. For the latter case also the influence of an intrinsic piezoelectric field and of the special symmetry properties of the wurtzite structure are discussed.