The kinetic Monte Carlo simulations were used to study the nucleation and growth mechanism of GaAs. The Ehrlich- Schwoebel (ES) barrier has an important effect on the growth mechanism. It was shown that the island density mainly depends on the growth temperature: low island density for high temperature, and high island density for low temperature. The islands in the second layer appear at small surface coverage for the high ES barrier or low temperature, while the islands appear at large surface coverage for the low ES barrier or high temperature. In GaAs epitaxial growth the critical size has its original meaning only for the low temperature and the high ES barrier. The single value of the critical size has to be replaced by two sizes in the two different directions because of the anisotropic surface migration. (c) 2006 Elsevier B.V. All rights reserved.