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

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.