The elemental nitridation process of alpha-Al2O3 surface is theoretically investigated by our ab inino-based approach incorporating the pregrowth conditions such as temperature and pressure. The calculated results for adsorption diagram imply that N atoms cannot adsorb on the alpha-Al2O3(0001) surface at all temperatures beyond 240 K supplying N-2 and N source gases. This suggests that the nitridation process cannot be interpreted only by N itself but should involve another contribution. To this end, we investigate stable surface structures as functions of N and O chemical potentials. The calculated surface diagram reveals that N atoms are easily incorporated on the alpha-Al2O3(0001) surface under pregrowth conditions such that O atoms tend to desorb from the surface. Moreover, the N adatoms are found to be easily substituted for O atoms located beneath the surface to form the AlN layer. Consequently, 0 desorption is crucial for nitridation process of alpha-Al2O3. This is consistent with some experimental findings reported previously. (C) 2012 Elsevier B.V. All rights reserved.