Method and apparatus to determine a patterning process parameter

A method, comprising:

• obtaining measurement results for different instances of a structure generated by a patterning process, wherein measurement results are obtained at each of a plurality of different set values of a patterning process parameter that measures a change in the physical configuration of the structure and each different set value of the patterning process parameter corresponds to a physical configuration of the structure that causes an asymmetric optical characteristic distribution in a radiation representation;
• and
• determining, by a hardware computer system, a plurality of data-driven values that correspond to weights for calculation with measured optical characteristic values of a further instance of the structure to calculate a value of the patterning process parameter, wherein the set values and the measurement results are used in an objective or merit function or a machine learning algorithm, to determine the data-driven values.

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

• obtain measurement results for different instances of a structure generated by a patterning process, wherein measurement results are obtained at each of a plurality of different set values of a patterning process parameter that measures a change in the physical configuration of the structure and each different set value of the patterning process parameter corresponds to a physical configuration of the structure that causes an asymmetric optical characteristic distribution in a radiation representation;
• and
• determine a plurality of data-driven values that correspond to weights for calculation with measured optical characteristic values of a further instance of the structure to calculate a value of the patterning process parameter, wherein the set values and the measurement results are used in an objective or merit function or a machine learning algorithm, to determine the data-driven values.

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

• use a mathematical model of a structure to predict an optical response when illuminating the structure with a radiation beam, the structure having geometric symmetry at a nominal physical configuration and a patterning process parameter measures change in the physical configuration;
• and
• execute a non-linear solver with values of, or derived from, the optical response to determine coefficients of a mathematical function of the patterning process parameter as a variable thereof, the determined coefficients and the mathematical function for use with a measured representation of detected radiation from the structure, on a substrate, at a different physical configuration than the nominal physical configuration which causes an asymmetric optical characteristic distribution in the detected representation, to determine a value of the patterning process parameter for the measured structure.