Electronic states in spherical GaN nanocrystals embedded in various dielectric matrices: The k ⋅ p-calculations

Abstract

Using the envelope-function approximation, the single-particle states of electrons and holes in spherical GaN nanocrystals embedded in different amorphous dielectric matrices (SiO2, Al2O3, HfO2 and Si3N4) have been calculated. Ground state energies of electrons and holes in GaN nanocrystals are determined using the isotropic approximation of the k ⋅ p -Hamiltonian. All the ground state energies are found to increase with lowering the nanocrystal size and are proportional to the R−n, where R is the nanocrystal radius, n =1.5-1.9 for electrons and 1.7-2.0 for holes. The optical gap of GaN nanocrystals changes from 3.8 to 5 eV for the nanocrystal radius ranging from 3 to 1 nm.

Effects of an external electric field on the electronic and optical properties of a Cylindrical ZnS/ZnO multi-layer quantum dot with a parabolic potential

“…What makes this model easy to choose is determined by several advantages such as the overall simplicity compared to other computational tools, while including all complexities such as the periodicity of the crystal, strain [19] in addition to the effect of remote bands in the effective mass tensor. However the (EFA) method has also some limitations, as it is applicable only to nanocrystals with radii more than approximately 1 nm [20], while author in Ref. [21] concluded that even though (EFA) is not perfectly accurate, it can be very useful from the conceptual point of view and often provides valuable physical insight.…”