Control substrate polishing using constrained cost function
Controlling a polishing system includes receiving 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, a polishing rate is determined for the region, and an adjustment is calculated for at least one processing parameter. Calculation of the adjustment includes minimizing a cost function that includes, for each region, 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 optimization of the cost function is subject to at least one constraint.
1 . A non-transitory computer readable medium having a computer program encoded therein, the computer program comprising instructions for causing one or more computers to:
cause a plurality of chambers in a carrier head of a polishing system to be pressurized to a plurality of pressures;
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;
calculate an adjustment to the polishing rate, wherein calculating the adjustment to the polishing rate comprises calculating a pressure adjustment for at least one pressure of the plurality of pressures, wherein calculation of the pressure adjustment includes minimizing a cost function that includes, for each region, 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 wherein optimization of the cost function is subject to a constraint that a pressure difference between two chambers of the plurality of chambers cannot exceed a maximum pressure difference; and
adjust the polishing rate by adjusting at least one pressure of the plurality of pressures according to the calculated pressure adjustment.
2 . The computer readable medium of claim 1 , wherein the optimization of the cost function is subject to a constraint that the pressure difference between two adjacent chambers of the plurality of chambers cannot exceed the maximum pressure difference.
3 . The computer readable medium of claim 1 , wherein optimization of the cost function is subject to a constraint that a pressure difference between a chamber of the plurality of chambers and an average pressure of multiple chambers cannot exceed a second maximum pressure difference.
4 . The computer readable medium of claim 3 , wherein optimization of the cost function is subject to a constraint that a pressure of a chamber of the plurality of chambers cannot exceed a maximum pressure or cannot fall below a minimum pressure.
5 . The computer readable medium of claim 1 , wherein the characterizing value is thickness.
6 . A non-transitory computer readable medium having a computer program encoded therein, the computer readable medium comprising instructions for causing one or more computers to:
cause a plurality of chambers in a carrier head of a polishing system to be pressurized to a plurality of pressures;
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;
calculate an adjustment to the polishing rate, wherein calculating the adjustment to the polishing rate comprises calculating a pressure adjustment for at least one pressure of the plurality of pressures, wherein calculation of the pressure adjustment includes minimizing a cost function that includes, for each region, 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 wherein optimization of the cost function is subject to a constraint that a pressure difference between a chamber of the plurality of chambers and an average pressure of multiple chambers cannot exceed a maximum pressure difference; and
adjust the polishing rate by adjusting at least one pressure of the plurality of pressures according to the calculated pressure adjustment.
7 . The computer readable medium of claim 6 , wherein the characterizing value is thickness.
8 . A polishing system, comprising:
a platen to support a polishing pad;
a carrier head to hold a substrate in contact with the polishing pad, the carrier head having a plurality of individually pressurizable chambers;
a motor to generate relative motion between the carrier head and the polishing pad;
an in-situ monitoring system to, for each region of a plurality of regions on the substrate being polished, generate a sequence of characterizing values for the region; and
a controller configured to
cause the plurality of individually pressurizable chambers in the carrier head to be pressurized to a plurality of pressures;
receive from the in-situ monitoring system, for each region of a plurality of regions on a substrate being processed by the polishing system, the sequence of characterizing values for the region;
for each region, determine a polishing rate for the region;
calculate an adjustment to the polishing rate, wherein calculating the adjustment to the polishing rate comprises calculating a pressure adjustment for at least one pressure of the plurality of pressures, wherein calculation of the pressure adjustment includes minimizing a cost function that includes, for each region, 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 wherein optimization of the cost function is subject to a constraint that a pressure difference between two chambers of the plurality of independently pressurizable chambers cannot exceed a maximum pressure difference; and
adjust the polishing rate by adjusting at least one pressure of the plurality of pressures according to the calculated pressure adjustment.
9 . The system of claim 8 , wherein the optimization of the cost function is subject to a constraint that the pressure difference between two adjacent chambers of the plurality of independently pressurizable chambers cannot exceed the maximum pressure difference.
10 . The system of claim 8 , wherein optimization of the cost function is subject to a constraint that a pressure difference between a chamber of the plurality of independently pressurizable chambers and an average pressure of multiple chambers cannot exceed a second maximum pressure difference.
11 . The system of claim 10 , wherein optimization of the cost function is subject to a constraint that a pressure of a chamber of the plurality of independently pressurizable chambers cannot exceed a maximum pressure or cannot fall below a minimum pressure.
12 . The system of claim 8 , wherein the characterizing value is thickness.
13 . A polishing system, comprising:
a platen to support a polishing pad;
a carrier head to hold a substrate in contact with the polishing pad, the carrier head having a plurality of individually pressurizable chambers;
a motor to generate relative motion between the carrier head and the polishing pad;
an in-situ monitoring system to, for each region of a plurality of regions on the substrate being polished, generate a sequence of characterizing values for the region; and
a controller configured to
cause the plurality of independently pressurizable chambers in the carrier head to be pressurized to a plurality of pressures;
receive from the in-situ monitoring system, for each region of a plurality of regions on a substrate being processed by the polishing system, the sequence of characterizing values for the region;
for each region, determine a polishing rate for the region;
calculate an adjustment to the polishing rate, wherein calculating the adjustment to the polishing rate comprises calculating a pressure adjustment for at least one pressure of the plurality of pressures, wherein calculation of the pressure adjustment includes minimizing a cost function that includes, for each region, 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 wherein optimization of the cost function is subject to a constraint that a pressure difference between a chamber of the plurality of independently pressurizable chambers and an average pressure of multiple chambers cannot exceed a maximum pressure difference; and
adjust the polishing rate by adjusting at least one pressure of the plurality of pressures according to the calculated pressure adjustment.
14 . The system of claim 13 , wherein the characterizing value is thickness.