We carried out theoretical analyses based on ab initio calculations that incorporate free energy of the vapor phase in order to determine the initial growth process of cubic GaN on GaN (0 0 1)-(4 x 1). The results suggest that a N-adsorbed structure appears at the initial growth stage and then Ga adsorbs on the N-adsorbed GaN (0 0 1)-(4 x 1) surface. Considering this process, we performed Monte Carlo simulations. The results suggest that the maximum point of Ga coverage after supplying a 1/32 monolayer of atoms shifted toward a Ga-rich condition from V/III = 1.0. (c) 2006 Elsevier B.V. All rights reserved.