Chemical mechanical polishing apparatus containing hydraulic multi-chamber bladder and method of using thereof

A method of polishing a substrate, comprising:

• chemically mechanically polishing a substrate in a polishing apparatus having a multi-chamber bladder including a plurality of chambers with a respective set of a cold liquid valve and a warm liquid valve, wherein each of the cold liquid valves is connected to a common cold liquid supply system configured to provide a cold liquid at a first temperature, and each of the warm liquid valves is connected to a common warm liquid supply system configured to provide a warm liquid at a second temperature that is higher than the first temperature, wherein each set of the cold liquid valve and the warm liquid valve is configured to provide a respective temperature control liquid obtained by mixing the cold liquid and the warm liquid at a respective mixing ratio for a respective one of the plurality of chambers;
• determining a temperature of the substrate at a plurality of locations on the substrate, thereby generating multiple measured values for the temperature of the substrate at the multiple locations of the substrate;
• and
• providing the respective temperature control liquid for each of the plurality of chambers of the multi-chamber bladder to cool the substrate at different cooling rates, thereby maintaining the substrate at substantially the same temperature while polishing the substrate, wherein the mixing ratio for each temperature control liquid for a respective one of the chambers is determined based at least in part on the multiple measured values for the temperature of the substrate at the multiple locations of the substrate.