During growth of submonolayer films of Co on Cu(111) at 280 K, the surface is damaged by etching, leading to an increase in the interfacial mixing and roughness. Bq means of a quantitative STM study, we analyze the influence of the temperature of the substrate on this etching. Our results for 18 ML of Co indicate that the etching rate is considerably reduced by lowering the substrate temperature to 140 K during Co deposition only, The total etched area observed after annealing the film to 300 K can be reduced by a factor of five, although the etching process continues at a much loa er rate. From the quantification of both the etched area and the Cu content within terrace islands, we argue that the etching is basically due to the diffusion of Cu atoms out of the step-edges. Such a diffusion process, which is significantly diminished at low temperature, takes place at the early stages of the growth, i.e. during Co aggregation and island formation. (C) 1998 Elsevier Science B.V. All rights reserved.