Validity of effective mass theory for energy levels in Si quantum wires

The dependence of the band gaps of Si wires on wire width is calculated within the effective mass theory, taking into account the finiteness of the barrier height of the confinement potential and the boundary conditions for the envelope functions at the interface between the wire and the confinement potential. Comparing the results with those of the first-principles calculation, we find that, with appropriate boundary conditions, the effective mass theory gives a good description of the electronic states in Si wires down to at least 10 Angstrom.