Method for tight-binding parametrization: Application to silicon nanostructures

We propose a method for tight-binding parametrization, designed to give accurate results in the calculation of confined edge states in semiconductor nanostructures of any size. Indeed, this improved tight-binding description accurately reproduces the bulk effective masses as well as the overall band structure. We apply it to the specific case of silicon. The electronic states of silicon nanostructures (films, wires, and dots), with various shapes and orientations, are calculated over large range of sizes (1-12 nm), including spin orbit. Accurate analytical laws for the confinement energies, valid over the whole range of sizes, are derived. Consistent comparison with the effective mass and k.p methods show that these are only of semiquantitative value even for sizes as large as 8 nm. The reasons for the failure of these techniques is analyzed in detail.