Method and system for providing tool induced shift using a sub-sampling scheme

A method for providing tool induced shift values across a semiconductor surface, comprising:

• generating a tool induced shift (TIS) sub-sampling scheme, wherein the TIS sub-sampling scheme is defined utilizing one or more statistical criterion, a selected number of sampling locations and a selected model type for TIS dependence across a semiconductor wafer surface, wherein the TIS sub-sampling scheme includes a set of measurement locations of the semiconductor wafer;
• determining a first set of TIS values by measuring TIS at each of the measurement locations of the generated TIS sub-sampling scheme;
• and
• determining a second set of TIS values by approximating TIS for each of a set of locations not included in the generated TIS sub-sampling scheme utilizing an interpolation process, wherein the interpolation process utilizes the first set of TIS values in order to calculate an approximated TIS value for each of the set of locations not included in the generated TIS sub-sampling scheme.

A method for providing tool induced shift values across a semiconductor surface, comprising:

• measuring overlay on at least one wafer of a lot of wafers at a first wafer orientation via an omniscient sampling process, wherein the omniscient sampling process includes measuring overlay at each measurement location of each field of the at least one wafer;
• generating a sub-sampling scheme by identifying a set of measurement locations having an overlay value between a first overlay value and a second overlay value, wherein the sub-sampling scheme includes a set of measurement locations of the at least one wafer;
• measuring overlay on the at least one wafer at a second wafer orientation rotated 180 degrees relative to the first wafer orientation at each of the measurement locations of the sub-sampling scheme;
• determining a first set of tool induced shift (TIS) values for the set of measurement locations of the sub-sampling scheme utilizing the overlay measured at the first wafer orientation and the overlay measured at the second wafer orientation rotated 180 degrees relative to the first wafer orientation;
• and
• determining a second set of TIS values by approximating TIS for each of a set of measurement locations of the at least one wafer not included in the generated sub-sampling scheme utilizing an interpolation process, wherein the interpolation process utilizes the first set of TIS values in order to calculate an approximated TIS value for each of the set of locations not included in the generated TIS sub-sampling scheme.

A method for providing tool induced shift values across a semiconductor surface, comprising:

• measuring overlay on at least one wafer of a lot of wafers at a first wafer orientation via an omniscient sampling process, wherein the omniscient sampling process includes measuring overlay at each measurement location of each field of the at least one wafer;
• generating a first set of process tool correctables utilizing one or more results of the overlay measured via the omniscient sampling process, wherein the first set of process tool correctables includes a process tool correctable calculated for each measurement location of each field of the at least one wafer, wherein a process tool correctable of the first set of process tool correctables associated with an analyzed measurement location of the at least one wafer is calculated using the measured overlay of all measurement locations of the at least one wafer;
• generating a second set of process tool correctables utilizing one or more results of the overlay measured via the omniscient sampling process, wherein the second set of process tool correctables includes a process tool correctable calculated for each measurement location of each field of the at least one wafer, wherein a process tool correctable of the second set of process tool correctables associated with an analyzed measurement location of the at least one wafer is calculated using the measured overlay of all measurement locations of the at least one wafer except for the analyzed measurement location;
• generating a sub-sampling scheme by comparing the first generated set of process tool correctables to the second generated set of process tool correctables, wherein the sub-sampling scheme includes a set of measurement locations, wherein the set of measurement locations of the sub-sampling scheme includes a selected number of sub-sampling measurement locations, wherein the selected number of measurement locations of the at least one wafer having the largest difference between the first generated set of process tool correctables and the second generated set of process tool correctables form the set of measurement locations of the sub-sampling scheme;
• measuring overlay on the at least one wafer at a second wafer orientation rotated 180 degrees relative to the first wafer orientation at each of the measurement locations of the generated sub-sampling scheme;
• determining a first set of tool induced shift (TIS) values for the set of sub-sampling measurement locations of the sub-sampling scheme utilizing the overlay measured at the first wafer orientation and the overlay measured at the second wafer orientation rotated 180 degrees relative to the first wafer orientation;
• and
• determining a second set of TIS values by approximating TIS for each of a set of locations of the at least one wafer not included in the generated sub-sampling scheme utilizing an interpolation process, wherein the interpolation process utilizes the first set of TIS values in order to calculate an approximated TIS value for each of the set of locations not included in the generated TIS sub-sampling scheme.