AbstractO atoms segregate to the surface during Cu homoepitaxial growth on Cu(001)-(2√2×√2)-O to retain the (2√2×√2) surface. The presence of an O adlayer on the Cu surface raises the barrier height for the surface diffusion of the Cu adatom and increases the transition temperature of the growth mode from step flow to layer by layer. The growth proceeds by site exchange between Cu adatoms and O atoms. The site-exchange rate competes with the Cu deposition rate. There exists a critical Cu deposition rate above which the O atoms can not exchange the sites with Cu adatoms. The critical Cu deposition rate obeys an Arrhenius relation and the active energy for the site-exchange is estimated at 0.66 eV.