From first principles we have examined the band offsets of selected zinc-bl
ende, wurtzite, and mixed zinc-blende/wurtzite GaN/AlN, GaN/SiC, and AlN/Si
C heterostructures, and their dependence on various structural and chemical
properties of the interfaces. Contrary to the case of the conventional, sm
all-gap, semiconductor heterojunctions, local atomic interfacial relaxation
has a major influence on the offsets of the polar heterovalent nitride sys
tems. However, provided this effect is taken into account, the band-offset
dependence on interface orientation, strain, and heterovalency can still be
qualitatively explained using linear-response-theory schemes. We also show
that a change in the band-gap discontinuity resulting from a cubic (111) t
o hexagonal (0001) polytype transformation in nitride heterostructures will
be selectively found in the conduction-band offset.