Density functional theory (DFT) calculations were carried out in order to study the adsorption and incorporation of scandium and yttrium atoms on the AlN(0001) surface aiming to gain insight into epitaxial growth of ScxAl1-xN and YxAl1-xN layers on AlN. The adsorption energy, geometry, formation energy, band structure and density of states of Sc (and Y) adatom/AlN(0001) systems are calculated. The calculations showed that the interaction between Sc (and Y) adatom and the AlN(0001) surface is strong (similar to 3.9 eV) and it prefers to adsorb on N-top site (T4). However, formation energy calculations reveal that the incorporation of Sc and Y atoms in the Al-substitutional site is energetically more favorable compared with the adsorption on the top layers, which can be attributed to the lower enthalpy of formation of ScN and YN with respect to that of AlN. The results also suggest that the Sc and Y atoms prefer to incorporate in top AlN surface layers. At full coverage, calculations show the formation of metallic ScxN and YxAl1-xN layers on the AlN polar surface over the entire range of Al chemical potentials, in agreement with experimental observations. In addition, we found that for high coverage Sc atoms couple ferromagnetically in the Al-substitutional sites on the AlN(0001) surface. (C) 2016 Elsevier B.V. All rights reserved.