A method of polishing a substrate member comprising a step of polishing a barrier layer containing tantalum, a tantalum alloy or a tantalum compound, by applying to the barrier layer a polishing medium for chemical-mechanical polishing, adapted to polish a barrier layer of tantalum, a tantalum alloy or a tantalum compound, which is a barrier layer for a conductor of copper, copper alloy, or copper oxide, the polishing medium comprising:
- an oxidizing agent;
- a protective-film-forming agent;
- abrasive grains;
- an acid;
- and
- water, wherein:
- said polishing medium has a pH of 3 or less, and
- said oxidizing agent is in a concentration of from 0.01% by weight to 3% by weight;
- and wherein:
- as a polishing condition, polishing pressure is 25 kPa and relative speed of substrate member to polishing platen is 18 m/minute, the polishing medium has:
- a polishing-rate ratio (Ta/Cu) between tantalum and copper or a copper alloy of more than 1;
- a polishing-rate ratio (TaN/Cu) between tantalum nitride and copper or a copper alloy of more than 1;
- a polishing-rate ratio (Ta/SiO2) between tantalum and silicon dioxide of more than 10;
- and
- a polishing-rate ratio (TaN/SiO2) between tantalum nitride and silicon dioxide film of more than 10.