Quantum-chemical calculations were carried out to shed more light upon possible first intermediates formed during chemical vapour deposition (CVD) processes leading to III-V semiconductors. Information about possible structures of intermediates and about thermodynamic properties in dependence of the temperature were collected. Because some of the systems calculated herein contain a substantial number of atoms (up to 144), it is limited to intermediates on the way to solid AIN. According to our suggestion, the first intermediates are species with the overall formula AINH2, Al2N2H4, Al3N3H6, AI5N5H8, AI7N7H, and Al9N9H, AI12N12H12. In further calculations the growth of a second layer, on top of the first layer, which is modelled by the Al12N12H12 cluster, is simulated. The Al12N12H12 "surface" offers two places for the attachment of an Al3N3H6 ring. At temperatures of 1000 K, the deltaG value for this attachment is only slightly negative, which suggests that the molecules can move relatively freely on the surface. This might be of importance for a defect-free growth process. Up to four layers are built on top of the first Al12N12H12 layer leading to Al24N24H24 (two layers), Al36N36H36 (three layers) and Al48N48H48 (four layers). The structures are compared with that of solid AIN in its most stable Wurzit-type structure.