The invention relates to an aqueous cleaning composition for wafers with copper wires that have been treated by chemical mechanical planarization in an integrated circuit processing, comprising 0.1 to 15 wt % of a nitrogen-containing heterocyclic organic base, 0.1 to 35 wt % of an alcohol amine and water. Upon contact with copper-containing semiconductor wafers that have been treated by chemical mechanical planarization for an effective period of time, the aqueous cleaning composition can effectively remove residual contaminants from the surfaces of the wafers, and simultaneously provide the copper-containing semiconductor wafers with a better surface roughness.