  Localized interface states in abrupt semiconductor heterojunctions are
studied within a tight-binding model. The intention is to provide a microscopic
foundation for the results of similar studies which were based upon the
two-band model within the envelope function approximation. In a two-dimensional
description, the tight-binding Hamiltonian is constructed such that the
Dirac-like bulk spectrum of the two-band model is recovered in the continuum
limit. Localized states in heterojunctions are shown to occur under conditions
equivalent to those of the two-band model. In particular, shallow interface
states are identified in non-inverted junctions with intersecting bulk
dispersion curves. As a specific example, the GaSb-AlSb heterojunction is
considered. The matching conditions of the envelope function approximation are
analyzed within the tight-binding description.
