Metrology parameter determination and metrology recipe selection

1. A method of determining a patterning process parameter from a metrology target, the method comprising:

obtaining a plurality of values of diffraction radiation from the metrology target, each value of the plurality of values corresponding to a different illumination condition of a plurality of illumination conditions of illumination radiation for the target; and

using, by a hardware computer system, the combination of values to determine a same value of the patterning process parameter for the target by solving a system of equations comprising each of the plurality of illumination conditions as a variable of at least one equation of the system of equations.

2. The method of claim 1 , wherein the values of diffraction radiation are obtained for each of at least four illumination conditions of the plurality of illumination conditions.

3. The method of claim 1 , wherein the target comprises at least two sub-targets, each sub-target having a different bias and each of the values correspond to diffraction radiation from a particular sub-target.

4. The method of claim 1 , wherein the values separately correspond to radiation of a positive value of a certain diffraction order of the diffraction radiation and to radiation of a negative value of the certain diffraction order of the diffraction radiation.

5. The method of claim 1 , wherein the system of equations comprises at least 16 equations.

6. The method of claim 1 , wherein the system of equations comprises at most 16 unknowns.

7. The method of claim 1 , wherein the target comprises an upper periodic structure and a lower periodic structure, wherein each equation of the system of equations comprises one or more terms that are a function of a variable representing amplitude of radiation from the lower periodic structure of the target and a variable representing phase of radiation from the target, and wherein at least an amplitude variable of radiation for a positive value of a certain diffraction order of the diffraction radiation is different from an amplitude variable of radiation for a negative value of the certain diffraction order of the diffraction radiation and at least a phase variable of radiation for the positive value of the certain diffraction order of the diffraction radiation is different from a phase variable of radiation for the negative value of the certain diffraction order of the diffraction radiation.

8. The method of claim 1 , wherein the target comprises a sub-target of the target with a positive bias of a periodic structure and a sub-target of the target with a negative bias of a periodic structure, wherein each equation of the system of equations comprises one or more terms that are a function of a variable representing amplitude of radiation from the target and a variable representing phase of radiation from the target, and wherein at least an amplitude variable of radiation for the sub-target with the positive bias is different from an amplitude variable of radiation for the sub-target with the negative bias and at least a phase variable of radiation for the sub-target with the positive bias is different from a phase variable of radiation for the sub-target with the negative bias.

9. The method of claim 1 , wherein each equation of the system of equations comprises one or more terms that are a function of a variable representing sensor asymmetry error.

10. The method of claim 9 , wherein at least a sensor asymmetry error variable of radiation for a positive value of a certain diffraction order of the diffraction radiation is different from a sensor asymmetry error variable of radiation for a negative value of the certain diffraction order of the diffraction radiation.

11. The method of claim 1 , wherein solving the system of equations comprises solving a nonlinear system of equations to arrive at the value of the patterning process parameter.

12. The method of claim 1 , wherein the patterning process parameter is overlay.

13. The method of claim 1 , wherein the values of diffraction radiation are diffraction values obtained from measurement of the metrology target on a substrate processed using a patterning process.

14. The method of claim 1 , wherein the values of diffraction radiation are diffraction values obtained from simulation of the measurement of the metrology target.

15. The method of claim 1 , wherein the illumination condition comprises wavelength and/or polarization.

16. The method of claim 1 , wherein the illumination condition comprises angle of incidence with respect to the target.

17. The method of claim 16 , wherein the plurality of values of diffraction radiation include those which each relate to a corresponding image, each of the images corresponding to a different non-overlapping illumination profile of the illumination radiation.

18. The method of claim 17 , wherein the images include one or more derived images, each of the one or more derived images being obtained from a linear combination of two or more acquired images so as to remove information relating to portions of an acquisition illumination profile of at least one of the acquired images which overlaps with an acquisition illumination profile relating to another of the acquired images, the acquisition illumination profiles comprising the actual illumination profiles used in acquisition of the acquired images.

19. A non-transitory computer program product comprising machine-readable instructions that, when executed by a processor system, are configured to cause the processor system to at least:

obtain a plurality of values of diffraction radiation from a metrology target, each value of the plurality of values corresponding to a different illumination condition of a plurality of illumination conditions of illumination radiation for the target; and

use the combination of values to determine a same value of a patterning process parameter for the target by solving of a system of equations comprising each of the plurality of illumination conditions as a variable of at least one equation of the system of equations.

20. A system comprising:

an inspection apparatus configured to provide a beam of radiation on a metrology target on a substrate and to detect radiation diffracted by the target; and

the non-transitory computer program product of claim 19 .

21. The system of claim 20 , further comprising a lithographic apparatus comprising a support structure configured to hold a patterning device to modulate a radiation beam and a projection optical system arranged to project the modulated radiation beam onto a radiation-sensitive substrate.

22. A non-transitory computer program product comprising machine-readable instructions that, when executed by a processor system, are configured to cause the processor system to at least:

obtain a plurality of values of diffraction radiation from a metrology target, each value of the plurality of values corresponding to each of at least four different illumination conditions of illumination radiation for the target, each of the at least four different illumination conditions being of same illumination parameter type; and

use the combination of values to determine a same value of a patterning process parameter for the target.

23. The computer program product of claim 22 , further solving a system of equations comprising each of the at least four different illumination conditions as a variable of at least one equation of the system of equations.