Methods for sample scheme generation and optimization

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.

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.

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.

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.

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.