  Compositionally graded interfaces in power electronic devices eliminate
dislocations, but they can also decrease thermal conduction, leading to
overheating. We quantify the thermal resistances of GaN/AlN graded interfaces
of varying thickness using ab initio Green's functions, and compare them with
the abrupt interface case. A non-trivial power dependence of the thermal
resistance versus interface thickness emerges from the interplay of alloy and
mismatch scattering mechanisms. We show that the overall behavior of such
graded interfaces is very similar to that of a thin-film of an effective alloy
in the length scales relevant to real interfaces.
