| CPC B24B 37/005 (2013.01) | 20 Claims |

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1. A computer program product for controlling a polishing system comprising a non-transitory computer readable medium comprising instructions for causing one or more computers to:
receive from an in-situ monitoring system, for each region of a plurality of regions on a substrate being processed by the polishing system, a sequence of characterizing values for the region;
for each region, determine a polishing rate for the region;
for each particular parameter update time of a plurality of parameter update times, calculate an adjustment for at least one polishing control parameter of the polishing system, wherein calculating the adjustment includes minimizing a cost function that includes, for each region
i) a difference between a current characterizing value or an expected characterizing value at an expected endpoint time and a target characterizing value for the region, and
ii) a plurality of projected future pressure changes to occur at parameter update times subsequent to the particular parameter update time for the region and/or a plurality of differences between projected future pressures to occur at parameter update times subsequent to the particular parameter update time and a baseline pressure for the region; and
for each particular parameter update time, adjust to the at least one polishing control parameter of the polishing system based on the calculated adjustment.
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