Provided herein are methods for using corrosion-inhibiting cleaning compositions for semiconductor wafer processing that include an aqueous admixture of at least water, a surfactant and a corrosion-inhibiting compound selected from a group consisting of amino phosphonates, polyamines and polycarboxylic acids. The quantity of the corrosion-inhibiting compound in the admixture is preferably in a range from about 0.0001 wt % to about 0.1 wt % and the quantity of the surfactant is preferably in a range from about 0.001 wt % to about 1.0 wt %. The aqueous admixture may also include sulfuric acid and a fluoride, which act as oxide etchants, and a peroxide, which acts as a metal etchant.