The incorporation of N atoms on GaAs(001)-(2 x 4)alpha 2 and -(3 x 3) surfaces under the growth conditions is theoretically investigated on the basis of surface phase diagrams which are obtained by comparing the adsorption energy given by ab initio calculations with the gas-phase chemical potentials. The calculated surface phase diagrams demonstrate that a single N-As dimer is formed on GaAs(001)-(2 x 4) and -(3 x 3) surfaces. Furthermore, two N atoms of surface are found to be substituted for As atoms located at the third layer of the surface. The analysis of stable structures reveals that the stability originates from the competition between energy profit in Ga-N bond formation and energy deficit in strain accumulation due to N located at the third layer. These results suggest that the bond energy as well as lattice strain are crucial for N incorporation processes on GaAs(001) substrate. (c) 2013 Elsevier B.V. All rights reserved.