The problem of theoretically predicting heterojunction band alignments has attracted a good deal of attention in recent years. The electron-affinity model proposed by Anderson [18] was generally accepted until about 1976. The first attempts to predict band lineups for a variety of heterojunctions based upon microscopic models were those of Frensley and Kroemer [30,31] and Harrison [32]. Since then, a large number of different approaches have been proposed and investigated. The interested reader should consult the reviews by Kroemer [29,19], Tersoff [33], and Yu, McCaldin, and McGill [23].
Most theories of the band alignment conceptually divide the problem into two
parts: the determination of the band-edge energies in the bulk with respect
to some reference energy, and the determination of the difference (if any)
between the reference energies across the heterojunction. An important
question from both the theoretical and experimental point of view, is
whether it is possible to define a universal scale for band energies which
would always give the correct heterojunction band alignment. If this were
the case, 
and 
would only depend upon the local chemical
composition, and not upon the other material participating in the
heterojunction under consideration. A useful concept by which this idea may
be experimentally tested is ``transitivity.'' Transitivity applies if one
may predict the band alignment of a junction AC knowing the band alignments of
junctions AB and BC, by
Most of the simpler theories of heterojunction band alignment possess transitivity, and it appears to be verified to within experimental uncertainties in lattice-matched heterostructure systems [28,24].
If transitivity holds within a given set of materials, then there must exist a universal energy scale for semiconductor energy bands, at least for that set of materials. It makes absolutely no difference where the origin of this scale is chosen. It is often convenient, since the band discontinuities are the experimentally measured quantities, to choose a given band edge of a major material, such as the valence-band edge of GaAs, as the reference energy.