Structural stability of GaN(0 0 0 1) under Ga-rich conditions is systematically investigated by using our ab initio-based approach. The surface phase diagram for GaN(0 0 0 1) including (2 x 2) and pseudo(1 x 1) is obtained as functions of temperature and Ga beam equivalent pressure by comparing chemical potentials of Ga atom in the gas phase with that on the surface. The calculated results reveal that the pseudo-(1 x 1) appearing below 684-973 K changes its structure to the (2 x 2) with Ga adatom at higher temperatures beyond 767-1078 K via the newly found (1 x 1) with two adlayers; of Ga. These results are consistent with the stable temperature range of both the pseudo-(1 x 1) and (2 x 2) with Ga adatom obtained experimentally. Furthermore, it should be noted that the structure with another coverage of Ga adatoms between the (1 x 1) and (2 x 2)-Ga does not appear as a stable structure of GaN(0 0 0 1). Furthermore, ghost island formation observed by scanning tunneling microscopy is discussed on the basis of the phase diagram. (C) 2009 Elsevier B.V. All rights reserved.