Empirical tight-binding calculation of the branch-point energy of the continuum of interface-induced gap states

The band lineup at metal–semiconductor contacts as well as at semiconductor heterostructures may be described by one and the same physical concept, the continuum of interface-induced gap states. These intrinsic interface states derive from the virtual gap states (ViGS) of the complex semiconductor band structure and their character varies from predominantly donorlike closer to the valence band to mostly acceptorlike nearer to the conduction band. Calculations are presented of the respective branch points for elemental and binary as well as ternary compound semiconductors which make use of Baldereschi’s concept of mean-value points in the Brillouin zone Phys. Rev. B 7, 5212 (1973), Penn’s idea of dielectric band gaps Phys. Rev. 128, 2093 (1962), and the empirical tight-binding approximation (ETB). The results are as follows. First, at the mean-value point the band gaps calculated in the GW approximation have the same widths as the dielectric band gaps. Second, the ETB approximation reproduces the GW valence-band energies at the mean-value point. Third, the branch points of the ViGS are slightly below midgap at the mean-value point. The ETB branch-point energies excellently reproduce the barrier heights of gold Schottky contacts on 19 semiconductors and the valence-band offsets of Al1−xGaxAs/GaAs heterostructures.