A method for the chemical-mechanical planarization of a substrate containing at least one copper layer, at least one ruthenium layer, and at least one tantalum or tantalum nitride layer comprising the steps of providing a chemical-mechanical polishing composition containing (a) at least one type of abrasive particles; (b) at least one oxidizing agent (b1) selected from persulfates and at least one oxidizing agent (b2) selected from periodates as the oxidizing agents wherein the oxidizing agent (b1) is capable of increasing the material removal rate of the tantalum or tantalum nitride layer and the other oxidizing agent (b2) is capable of reacting with the ruthenium layer, and to simultaneously form a strong oxide film on the copper surface; (c) at least one pH adjusting agent; (d) deionized water; (e) optionally comprising at least one antioxidant, wherein the pH of the chemical-mechanical polishing composition ranges from 5 to 8; contacting the substrate surface containing at least one copper layer, at least one ruthenium layer, and at least one tantalum or tantalum nitride layer to be polished with the chemical-mechanical polishing composition and a polishing pad; and chemically and mechanically polishing the substrate surface containing at least one copper layer, at least one ruthenium layer, and at least one tantalum or tantalum nitride layer by way of moving the polishing pad relative to the substrate. providing a chemical-mechanical polishing composition containing (a) at least one type of abrasive particles; (b) at least one oxidizing agent (b1) selected from persulfates and at least one oxidizing agent (b2) selected from periodates as the oxidizing agents wherein the oxidizing agent (b1) is capable of increasing the material removal rate of the tantalum or tantalum nitride layer and the other oxidizing agent (b2) is capable of reacting with the ruthenium layer, and to simultaneously form a strong oxide film on the copper surface; (c) at least one pH adjusting agent; (d) deionized water; (e) optionally comprising at least one antioxidant, wherein the pH of the chemical-mechanical polishing composition ranges from 5 to 8; (a) at least one type of abrasive particles; (b) at least one oxidizing agent (b1) selected from persulfates and at least one oxidizing agent (b2) selected from periodates as the oxidizing agents wherein the oxidizing agent (b1) is capable of increasing the material removal rate of the tantalum or tantalum nitride layer and the other oxidizing agent (b2) is capable of reacting with the ruthenium layer, and to simultaneously form a strong oxide film on the copper surface; (c) at least one pH adjusting agent; (d) deionized water; (e) optionally comprising at least one antioxidant, contacting the substrate surface containing at least one copper layer, at least one ruthenium layer, and at least one tantalum or tantalum nitride layer to be polished with the chemical-mechanical polishing composition and a polishing pad; and chemically and mechanically polishing the substrate surface containing at least one copper layer, at least one ruthenium layer, and at least one tantalum or tantalum nitride layer by way of moving the polishing pad relative to the substrate. <EOS>