Method and apparatus to reduce effects of nonlinear behavior

1. A method comprising:

obtaining information regarding a patterning error in a patterning process involving a patterning device;

determining a nonlinearity over a period of time introduced by modifying the patterning error by a modification apparatus according to the patterning error information;

determining, by a hardware computer system, a patterning error offset for use with the modification apparatus based on the determined nonlinearity, wherein the patterning error offset comprises a static patterning error offset that doesn't vary over the period of time; and

outputting an electronic or optical signal pertaining to at least part of the patterning error offset toward at least part of the modification apparatus for modifying the patterning error.

2. The method of claim 1 , wherein a maximum of the nonlinearity over the period of time is reduced by combination of at least part of the patterning error offset and the modification of the patterning error by the modification apparatus.

3. The method of claim 2 , wherein the combination yields a patterning error for correction by the modification apparatus at the beginning of the period of time having a substantially equal absolute value as a patterning error for correction by the modification apparatus at the end of the period of time.

4. The method of claim 1 , further comprising creating first modification information for modification of the patterning device based on the patterning error offset, wherein at least part of the patterning error offset is combined with the modification of patterning error by the modification apparatus when the patterning device is used in the patterning process after modification according to the first modification information.

5. The method of claim 1 , wherein the patterning error offset comprises a dynamic patterning error offset that changes over the period of time.

6. The method of claim 1 , further comprising creating second modification information for a manufacturing processing tool used in the patterning process based on the patterning error offset, wherein at least a portion of the patterning error offset is combined with the modification of the patterning error by the modification apparatus when the manufacturing processing tool is used in the patterning process and modified according to the second modification information.

7. The method of claim 6 , wherein the manufacturing processing tool comprises a track tool, a deposition tool, a planarization tool and/or an etch tool.

8. The method of claim 1 , further comprising:

apportioning, by the computer system, at least a part of the patterning error among at least two modification apparatuses of a patterning system; and

creating, by the computer system, modification information for at least one of the at least two modification apparatuses of the patterning system according to the apportionment and the patterning error offset.

9. The method of claim 1 , wherein the patterning error is time-varying and a correction of the patterning error by the modification apparatus without at least part of the patterning error offset does, or would, fall outside a modification range of the modification apparatus.

10. The method of claim 1 , wherein the nonlinearity changes over the period of time.

11. The method of claim 1 , wherein obtaining the patterning error information comprises obtaining the patterning error information by measurement and/or by simulation.

12. The method of claim 1 , wherein the patterning error comprises one or more selected from: critical dimension information, overlay error information, focus information, and/or dose information.

13. A non-transitory computer readable storage medium storing machine-readable instructions, wherein when executed, the machine-readable instructions cause the processor system to at least:

determine a nonlinearity over a period of time introduced by modifying a patterning error, in a patterning process involving a patterning device, by a modification apparatus according to information obtained regarding the patterning error;

determine a patterning error offset for use with the modification apparatus based on the determined nonlinearity, wherein the patterning error offset comprises a static patterning error offset that doesn't vary over the period of time; and

output an electronic or optical signal pertaining to at least part of the patterning error offset toward at least part of the modification apparatus for modifying the patterning error.

14. The computer readable storage medium of claim 13 , wherein a maximum of the nonlinearity over the period of time is reduced by combination of at least part of the patterning error offset and the modification of the patterning error by the modification apparatus.

15. A method comprising:

obtaining information regarding a nonlinearity over a period of time, wherein the nonlinearity is caused at least in part by a modification apparatus modifying a patterning error;

apportioning, by a hardware computer system, at least a part of the patterning error for correction among at least two modification apparatuses of a patterning system based on the nonlinearity;

creating, by the computer system, modification information for at least one of the at least two modification apparatuses of the patterning system according to the apportionment, the at least one modification apparatus configured to modify the patterning error based on the modification information; and

outputting an electronic or optical signal pertaining to at least part of the modification information toward at least part of the at least one of the at least two modification apparatuses for modifying the patterning error.

16. The method of claim 14 , wherein the modification information for the at least one modification apparatus creates a patterning error offset such that a combination of the patterning error offset with the modification of patterning error by at least one other modification apparatus yields a reduction in nonlinearity over the period of time for the at least one other modification apparatus.

17. The method of claim 14 , wherein a maximum of the nonlinearity over the period of time is reduced by modification of the at least one modification apparatus according to the modification information.

18. The method of claim 17 , wherein modification of the at least one modification apparatus according to the modification information yields a patterning error for correction by at least one other modification apparatus at the beginning of the period of time having a substantially equal absolute value as a patterning error for correction by the at least one other modification apparatus at the end of the period of time.

19. The method of claim 14 , further comprising creating modification information for modification of the patterning device based on the apportionment or nonlinearity, wherein the patterning device is used in the patterning process after modification according to the modification information.

20. The method of claim 15 , wherein the patterning error is time-varying and a correction of the patterning error by at least one other modification apparatus without modification of the at least one modification apparatus does, or would, fall outside a modification range of the at least one other modification apparatus.

21. A non-transitory computer readable storage medium storing machine-readable instructions, wherein when executed, the machine-readable instructions cause the processor system to at least:

obtain information regarding a nonlinearity over a period of time, wherein the nonlinearity is introduced from modifying a patterning error;

apportion at least a part of the patterning error for correction among at least two modification apparatuses of a patterning system based on the nonlinearity;

create modification information for at least one of the at least two modification apparatuses of the patterning system according to the apportionment, the at least one modification apparatus configured to modify the patterning error based on the modification information; and

output an electronic or optical signal pertaining to at least part of the modification information toward at least part of the at least one of the at least two modification apparatuses apparatus for modifying the patterning error.