Theoretical study of electronic structure of silicon nanocrystals

We report on a theoretical study of the electronic structure of silicon nanocrystals with a shape of the regular rhombic dodecahedron, based on a tight-binding method. The energies of the lowest unoccupied state and the highest occupied state have been calculated. We have shown that the six-fold degenerate conduction band minima of the bulk silicon crystal are split into a non-degenerate A(1) state, a double-degenerate E state and a triple-degenerate T-2 state and that the ordering of the energies of these states depends on the size of the silicon nanocrystal. Thus the lowest unoccupied state of the silicon nanocrystal can have different symmetries at different nanocrystal sizes. However. as the size of the nanocrystal changes, the symmetry of the highest occupied state remains the same; it is T-2 symmetric. The wave functions of the lowest unoccupied and highest occupied states have also been calculated. It is shown that these states have very different localization properties. The wave function of the lowest unoccupied A(1) state is largely localized on the central atomic site and on its nearest neighbors. In contrast, the wave function of the lowest unoccupied E state has no contribution from the orbitals of the central atom. Furthermore, the wave functions of both the lowest unoccupied and the highest occupied T-2 states are distributed more evenly over a large portion of the silicon nanocrystals.