ABSTRACTSynchrotron X-ray scattering was used to study the temperature and coverage dependence of the root-mean-square (rms) surface roughness, σ, during the homoepitaxial growth on Cu(001). At temperatures between 370 and 160K, the rms roughness was found to increase as a power law, σ =Θβ, with the coverage Θ. The roughness exponent, β, amounts to ∼1/2 for T≤200K, and it monotonically decreases with increasing T, reaching β∼1/3 at T=370K. The mean-square roughness measured at a constant coverage of 15ML, σ2 15 ML, also depends on the temperature of the substrate: between 370 and 200K, σ2 15 ML becomes progressively larger at lower temperatures, but at 110K a reentrant smoother growth is observed.