  Starting with empirical tight-binding band structures, the branch-point (BP)
energies and resulting valence band offsets (VBOs) for the zincblende phase of
InN, GaN and AlN are calculated from their k-averaged midgap energy.
Furthermore, the directional dependence of the BPs of GaN and AlN is discussed
using the Green's function method of Tersoff. We then show how to obtain the
BPs for binary semiconductor alloys within a band-diagonal representation of
the coherent potential approximation (CPA) and apply this method to cubic AlGaN
alloys. The resulting band offsets show good agreement to available
experimental and theoretical data from the literature. Our results can be used
to determine the band alignment in isovalent heterostructures involving pure
cubic III-nitrides or AlGaN alloys for arbitrary concentrations.
