Elementary calculation of the branch-point energy in the continuum of interface-induced gap states

The band alignment at ideal semiconductor interfaces may be described by the continuum of interface-induced gap states. These intrinsic interface states derive from the virtual gap states (ViGS) of the complex semiconductor band structure. The energy at which their character changes from predominantly donorlike to acceptor-like is defined as their branch point. This branch point is located slightly below the middle of its band gap at the mean-value point in the Brillouin zone. By comparison with GW band-structure data it is demonstrated that, first, the width of the band gap at the mean-value point equals the dielectric band gap and that, second, the empirical tight-binding approximation reproduces the dispersion of the GW valence bands from the middle to the mean-value point of the Brillouin zone. Branch points computed by Tersoff for 15 semiconductors are found slightly below the middle of the respective dielectric band gaps at the mean-value point of the Brillouin zone. These results make possible simple calculations of branch points for other zincblende-structure semiconductors.