The effect of a monolayer thick SiN film on the surface states of the AlN/GaN heterostructure grown by molecular beam epitaxy was investigated. It was revealed that the submonolayer SiN coating of the AlN surface leads to the formation of an ordered (√3 × √3)R30° structure. Further SiN film growth results in a Si-enriched SiN amorphous film formation. The Fermi level, pinned 1 eV above the valence band maximum of as-grown AlN, jumps 2.3 eV when (√3 × √3)R30° is formed, and then gradually goes to 3.1 eV with an increase in the thickness of the SiN film up to four monolayers. This is explained by the evolution of surface states, as well as the appearance of donor-like states in a Si-enriched SiN film. The presence of donor-like states was confirmed when studying the effect of current collapse in enhancement-mode high electron mobility transistors made of SiN/AlN/GaN heterostructures.