Methods for sample scheme generation and optimization

1. A method comprising:

obtaining measurement data associated with a set of locations;

analyzing the measurement data to determine statistically different groups of the locations; and

configuring, by a hardware computer system, a sample scheme generation algorithm based on the statistically different groups.

2. The method of claim 1 , wherein the locations in a group together define one or more regions within a field, the field being repeated across one or more substrates.

3. The method of claim 1 , wherein:

the locations in a group together define one or more regions spanning a plurality of fields across one or more substrates, the plurality of fields having different respective sub-sampling in a sampling scheme generated by the sample scheme generation algorithm; and

the analyzing the measurement data comprises stacking the measurement data across the spanned plurality of fields using their different respective sub-sampling to determine the statistically different groups of the locations.

4. The method of claim 1 , wherein the sample scheme generation algorithm comprises a genetic algorithm.

5. The method of claim 4 , wherein the configuring comprises configuring a crossover operator to swap sampling information between the determined statistically different groups.

6. The method of claim 4 , wherein the configuring comprises configuring a mutation operator to mutate sampling information in a selected determined statistically different group.

7. The method of claim 4 , wherein the sample scheme generation algorithm comprises a multi-objective genetic algorithm and the method further comprises:

obtaining a constraint associated with a sample scheme across one or more substrates; and

using the constraint as an input to the sample scheme generation algorithm.

8. The method of claim 4 , wherein the sample scheme generation algorithm comprises a multi-objective genetic algorithm and the method further comprises:

obtaining a plurality of key performance indicators associated with a sample scheme across one or more substrates; and

using the key performance indicators in a fitness function in the sample scheme generation algorithm.

9. The method of claim 8 , wherein the fitness function comprises a comparison between the key performance indicators calculated for the measurement data of the set of locations and the key performance indicators calculated for a reduced sample scheme individual.

10. The method of claim 1 , wherein the set of locations is defined across one or more substrates.

11. The method of claim 1 , wherein the set of locations is defined across one or more fields.

12. The method of claim 11 , wherein the measurement data comprises values of a parameter measured across a field by a sensor within an optical plane.

13. The method of claim 12 , wherein the parameter is one of: an aberration level, a dose, a focus level or a detected position of a mark.

14. A computer program product comprising a non-transitory computer-readable medium having computer instructions therein, the instructions, when executed by a computer system, configured to cause the computer system to at least:

obtain measurement data associated with a set of locations;

analyze the measurement data to determine statistically different groups of the locations; and

configure a sample scheme generation algorithm based on the statistically different groups.

15. A method comprising:

obtaining measurement data associated with one or more substrates;

obtaining (i) a constraint associated with a sample scheme across one or more substrates, or (ii) a plurality of key performance indicators associated with a sample scheme across one or more substrates, or (iii) both (i) and (ii); and

using, by a hardware computer system, the constraint, or the plurality of key performance indicators, or both the constraint and the plurality of key performance indicators, in a sample scheme generation algorithm configured to determine samples to be measured, the sample scheme generation algorithm comprising a multi-objective genetic algorithm configured to process the measurement data.

16. The method of claim 15 , further comprising:

obtaining measurement data associated with a set of locations across one or more substrates;

analyzing the measurement data; and

optimizing a sample scheme based on the analysis,

wherein the locations define one or more regions spanning a plurality of fields across one or more substrates, the plurality of fields having different respective sub-sampling in the sampling scheme;

wherein the constraint is based on the analysis; and

wherein the analyzing the measurement data comprises stacking the measurement data across the spanned plurality of fields using their different respective sub-sampling.

17. The method of claim 16 , wherein the optimizing the sample scheme comprises configuring a crossover operator of a sample scheme generation algorithm to swap sampling information between the fields.

18. The method of claim 16 , wherein the optimizing the sample scheme comprises configuring a mutation operator of a sample scheme generation algorithm to mutate sampling information in a selected field.

19. A method comprising:

obtaining measurement data associated with a set of locations across one or more substrates;

analyzing the measurement data; and

optimizing, by a hardware computer system, a sample scheme based on the analysis,

wherein the locations define one or more regions spanning a plurality of fields across one or more substrates, the plurality of fields having different respective sub-sampling in the sampling scheme, and

wherein the analyzing the measurement data comprises stacking the measurement data across the spanned plurality of fields using their different respective sub-sampling.

20. A computer program product comprising a non-transitory computer-readable medium having computer instructions therein, the instructions, when executed by a computer system, configured to cause the computer system to at least:

obtain measurement data associated with a set of locations across one or more substrates;

analyze the measurement data; and

optimize a sample scheme based on the analysis,

wherein the locations define one or more regions spanning a plurality of fields across one or more substrates, the plurality of fields having different respective sub-sampling in the sampling scheme, and

wherein the analysis of the measurement data comprises stacking of the measurement data across the spanned plurality of fields using their different respective sub-sampling.

21. A computer program product comprising a non-transitory computer-readable medium having computer instructions therein, the instructions, when executed by a computer system, configured to cause the computer system to at least:

obtain measurement data associated with one or more substrates;

obtain aa constraint associated with a sample scheme across one or more substrates, or (ii) a plurality of key performance indicators associated with a sample scheme across one or more substrates, or (iii) both (i) and (ii); and

use the constraint and/or the plurality of key performance indicators in a sample scheme generation algorithm comprising a multi-objective genetic algorithm configured to process the measurement data.