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The kinetics of Al and N adatoms on reconstructed AlN(0001) surfaces under growth conditions is investigated by performing first-principles pseudopotential calculations. Our calculations reveal that the adsorption of Al adatom strongly depends on the surface reconstruction while its diffusion is not affected by the reconstruction: the adsorption of Al adatom on the surface under N-rich conditions is much easier than that under H-rich conditions. These results indicate that the growth of AlN during metal-organic vapor-phase epitaxy is prominent under N-rich conditions rather than H-rich conditions, consistent with experimentally reported growth rate difference.