Wide process range library for metrology

1. A method of generating a wide process range library for metrology of repeating structures on a semiconductor substrate or wafer, the method comprising:

generating, using a computer, a first library having a first process range for a first parameter;

generating a second library having a second process range for the first parameter, the second process range overlapping with the first process range;

stitching the second library to the first library to generate a third library having a third process range for the first parameter, the third process range wider than each of the first and second process ranges, the stitching comprising determining an overlap amount of the first and second process ranges based on a derivative of a combined function in a region where the second process range is overlapping with the first process range; and

providing a simulated spectrum from the third library.

2. The method of claim 1 , wherein the first library has one or more sub-libraries, the second library has one or more sub-libraries, and the third library includes all of the sub-libraries of the first and second libraries.

3. The method of claim 1 , wherein the first library has one or more additional parameters, the second library also has the one or more additional parameters, and the process ranges for the one or more additional parameters are the same in both the first and second libraries.

4. The method of claim 3 , wherein the first and second libraries differ only by the first and second process ranges.

5. The method of claim 1 , wherein

the stitching further comprises determining a library error estimation for each of the first and second libraries.

6. The method of claim 1 , the method further comprising:

generating a fourth library having a fourth process range for the first parameter, the fourth process range overlapping with the third process range; and

stitching the fourth library to the third library to generate a fifth library having a fifth process range for the first parameter, the fifth process range wider than each of the third and fourth process ranges.

7. The method of claim 1 , wherein the first library has a fourth process range for a second parameter, the second library has a fifth process range for the second parameter, the fifth process range overlapping with the fourth process range, and the third library has a sixth process range for the second parameter, the sixth process range wider than each of the fourth and fifth process ranges.

8. The method of claim 1 , wherein the first parameter is of an individual feature of a two-dimensional or three-dimensional grating structure.

9. The method of claim 8 , wherein the first parameter is selected from the group consisting of width, height, length, top corner rounding, bottom footing, and sidewall angle of the individual feature.

10. The method of claim 1 , further comprising:

comparing the simulated spectrum to a sample spectrum.

11. A method of generating a wide process range library for metrology of repeating structures on a semiconductor substrate or wafer, the method comprising:

generating, using a computer, a first library having a plurality of process ranges, each process range corresponding to a different one of a plurality of parameters;

generating a second library having a process range for a first of the plurality of parameters, the process range of the second library different from but overlapping with the process range of the first library for the first of the plurality of parameters;

stitching the second library to the first library, the stitching comprising determining an overlap amount of the first and second process ranges based on a derivative of a combined function in a region where the second process range is overlapping with the first process range;

repeating the generating and stitching for one or more additional parameters of the plurality of parameters to provide a final library; and

providing a simulated spectrum from the final library.

12. The method of claim 11 , wherein each of the process ranges of the final library is wider than or equal to the corresponding process range of the plurality of process ranges of the first library.

13. The method of claim 11 , further comprising:

comparing the simulated spectrum to a sample spectrum.

14. A non-transitory machine-accessible storage medium having instructions stored thereon which cause a data processing system to perform a method of generating a wide process range library for metrology of repeating structures on a semiconductor substrate or wafer, the method comprising:

generating a first library having a first process range for a first parameter;

generating a second library having a second process range for the first parameter, the second process range overlapping with the first process range; and

stitching the second library to the first library to generate a third library having a third process range for the first parameter, the third process range wider than each of the first and second process ranges, the stitching comprising determining an overlap amount of the first and second process ranges based on a derivative of a combined function in a region where the second process range is overlapping with the first process range.

15. The non-transitory storage medium as in claim 14 , wherein the first library has one or more sub-libraries, the second library has one or more sub-libraries, and the third library includes all of the sub-libraries of the first and second libraries.

16. The non-transitory storage medium as in claim 14 , wherein the first library has one or more additional parameters, the second library also has the one or more additional parameters, and the process ranges for the one or more additional parameters are the same in both the first and second libraries.

17. The non-transitory storage medium as in claim 16 , wherein the first and second libraries differ only by the first and second process ranges.

18. The non-transitory storage medium as in claim 14 , wherein

the stitching further comprises determining a library error estimation for each of the first and second libraries.

19. The non-transitory storage medium as in claim 14 , the method further comprising:

generating a fourth library having a fourth process range for the first parameter, the fourth process range overlapping with the third process range; and

stitching the fourth library to the third library to generate a fifth library having a fifth process range for the first parameter, the fifth process range wider than each of the third and fourth process ranges.

20. The non-transitory storage medium as in claim 14 , wherein the first library has a fourth process range for a second parameter, the second library has a fifth process range for the second parameter, the fifth process range overlapping with the fourth process range, and the third library has a sixth process range for the second parameter, the sixth process range wider than each of the fourth and fifth process ranges.

21. The non-transitory storage medium as in claim 14 , wherein the first parameter is of an individual feature of a two-dimensional or three-dimensional grating structure.

22. The non-transitory storage medium as in claim 21 , wherein the first parameter is selected from the group consisting of width, height, length, top corner rounding, bottom footing, and sidewall angle of the individual feature.

23. The non-transitory storage medium as in claim 14 , wherein the third library comprises a simulated spectrum, the method further comprising:

comparing the simulated spectrum to a sample spectrum.

24. A non-transitory machine-accessible storage medium having instructions stored thereon which cause a data processing system to perform a method of generating a wide process range library for metrology of repeating structures on a semiconductor substrate or wafer, the method comprising:

generating a first library having a plurality of process ranges, each process range corresponding to a different one of a plurality of parameters;

generating a second library having a process range for a first of the plurality of parameters, the process range of the second library different from but overlapping with the process range of the first library for the first of the plurality of parameters;

stitching the second library to the first library, the stitching comprising determining an overlap amount of the first and second process ranges based on a derivative of a combined function in a region where the second process range is overlapping with the first process range; and

repeating the generating and stitching for one or more additional parameters of the plurality of parameters to provide a final library.

25. The non-transitory storage medium as in claim 24 , wherein each of the process ranges of the final library is wider than or equal to the corresponding process range of the plurality of process ranges of the first library.

26. The non-transitory storage medium as in claim 24 , wherein the final library comprises a simulated spectrum, the method further comprising:

comparing the simulated spectrum to a sample spectrum.