Polishing apparatus and polishing method

A polishing apparatus, comprising:

• at least one polishing unit including a polishing table for supporting a polishing pad, and
• a substrate holder for pressing a substrate against the polishing pad, the substrate holder including an elastic membrane film to form a plurality of pressure chambers for pressing the substrate, a head body to which the elastic membrane is attached, and a retainer ring arranged so as to surround the substrate;
• a film thickness measuring device configured to measure a film thickness profile of the substrate;
• and
• a controller configured to control at least operations of the polishing unit and the film thickness measuring device, the controller further configured to perform the operations comprising:
• storing in advance, with respect to polishing of the substrate, a response model which is created based on variations in an amount of polishing between monitored areas of the substrate due to variations in a pressure of a pressurized fluid supplied to each of the pressure chambers, the response model calculating predicted polishing amounts in each of the monitored areas, and
• obtaining the film thickness profile of the substrate before polishing by use of the film thickness measuring device;
• causing the substrate to be polished with an optimized polishing recipe including at least the pressures of the pressurized fluid supplied to each of the plurality of pressure chambers and a polishing time, the optimized polishing recipe being created based on the response model and a target polishing amount, which is a difference between the film thickness profile of the substrate before polishing and a target film thickness of the substrate;
• and
• causing a next substrate to be polished with a new optimized polishing recipe which is created based on a target polishing amount of the next substrate and a response model corrected by use of the optimized polishing recipe so as to match the predicted polishing amounts with actual polishing amounts, and the film thickness profile of the substrate before polishing and a film thickness profile of the substrate after polishing, the new optimized polishing recipe including at least the pressures of the pressurized fluid supplied to each of the plurality of pressure chambers and the polishing time,
• wherein the response model comprises an equation R, where R=Tp·(C·X+D), wherein R represents a matrix consisting of the predicted polishing amounts in each of the monitored areas of the substrate, Tp represents the polishing time, C represents a matrix consisting of response coefficients in each of the monitored areas of the substrate, X represents a matrix consisting of the pressures of the pressurized fluid supplied to each of the pressure chambers, and D represents a matrix consisting of offset amounts of each of the monitored areas in the substrate,
• the response coefficients are amounts of increase in a polishing rate per unit polishing pressure, and
• the respective offset amount is calculated such that a predicted polishing rate is equal to an actual polishing rate obtained by polishing of the substrate with a reference polishing recipe.