The formation energies, the intra- and inter-layer self-diffusion activation energies of a single vacancy in Fe (1 1 1) surface have been investigated with the modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface is down to the sixth layer for the formation and intra-layer migration of the vacancy. It is easier for a vacancy to form and to migrate in intra-layer in the first (especially), the second and the third layer. For inter-layer migration, a single vacancy in each of the first six layers is favorable to migrate to the upper layers. On the contrary, a single vacancy in the seventh, the eighth and the ninth layers is favorable to migrate to the lower layers. (c) 2007 Elsevier B.V. All rights reserved.