Caching of intra-layer calculations for rapid rigorous coupled-wave analyses

1. A method of generating a library of simulated-diffraction signals for an integrated circuit periodic grating, comprising:

generating sets of intermediate layer data,

wherein each set of intermediate layer data corresponds to a separate one of a plurality of hypothetical layers of a hypothetical profile of the periodic grating, and

wherein each separate hypothetical layer has one of a plurality of possible combinations of hypothetical values of properties for that hypothetical layer;

storing the generated sets of intermediate layer data; and generating simulated-diffraction signal, for each of a plurality of hypothetical profiles based on the stored generated sets of intermediate layer data.

2. The method of claim 1 , wherein generating sets of intermediate layer data comprise:

for each, hypothetical layer:

setting permittivity parameters;

computing a wave-vector matrix, the wave vector matrix being based on the permittivity parameters for the hypothetical layer; and

computing characteristic parameter for the wave-vector matrix computed for the hypothetical layer,

wherein the intermediate layer data for each hypothetical layer includes the characteristic parameters for the wave-vector matrix for that hypothetical layer.

3. The method of claim 2 , wherein generating sets of intermediate layer data comprise:

for each hypothetical layer:

setting incident-radiation parameter,

wherein the wave-vector matrix is based on the incident-radiation parameter.

4. The method of claim 1 , wherein generating sets of intermediate layer data comprise:

for each set of intermediate layer data:

computing at least one of:

permittivity parameters including a permittivity, harmonic components of the permittivity , and a permittivity harmonics matrix; and

inverse-permittivity parameters including in inverse-permittivity, harmonic components of the inverse-permittivity, and an inverse-permittivity harmonica matrix;

computing a wave-vector matrix; and

computing eigenvectors and eigenvalues of the wave-vector matrix to form an eigenvector matrix, a root-eigenvalue matrix and a compound matrix,

wherein the stored intermediate layer data includes the wave-vector matrix corresponding to that intermediate layer data.

5. The method of claim 4 , wherein generating simulated-diffraction signals comprises:

for each hypothetical profile:

constructing a matrix equation from the stored intermediate layer data corresponding to the hypothetical layers of the hypothetical profile, the matrix equation being a function of the stored eigenvector matrices, the computed root-eigenvalue matrices and the compound matrix;

solving the constructed matrix equation to determine a diffracted reflectivity value Ri for each harmonic order i; and

using the determined diffracted reflectivity values Ri to generate the simulated-diffraction signal for the hypothetical profile.

6. The method of claim 1 , wherein generating simulated-diffraction signals for each of a plurality of hypothetical profiles comprises:

constructing a matrix equation from the stored intermediate data corresponding to the hypothetical layers of the hypothetical profile; and

solving the constructed matrix equation to determine diffracted reflectivity values for the hypothetical profile.

7. The method of claim 1 , wherein generating simulated-diffraction signals for each of a plurality of hypothetical profile comprises:

performing rigorous coupled-wave analysis on the saved intermediate data corresponding to the hypothetical layers of the hypothetical profile.

8. The method of claim 1 , wherein storing the generated sets of intermediate layer data comprises:

storing the intermediate layer data within a cache.

9. The method of claim 8 , wherein the cache resides in a computer memory.

10. The method of claim 1 , wherein generating simulated-diffraction signals comprises:

characterizing the shape of a hypothetical profile for the periodic grating with a set of profile parameter; and

varying the set of profile parameters to generate the plurality of hypothetical profiles.

11. The method of claim 1 , wherein generating simulated-diffraction signals comprise:

for each hypothetical profile,

retrieving the one or more stored intermediate layer data that charactetizes the hypothetical profile; and

applying boundary conditions to generate a simulated-diffraction signal for the hypothetical profile.

12. The method of claim 11 further comprising:

pairing each hypothetical profile with the simulated-diffraction signal generated for that hypothetical profile, and

storing the hypothetical profile and simulated-diffraction signal pair.

13. The method of claim 12 , wherein the hypothetical profile and simulated-diffraction signal pair is stored in a computer-readable medium.

14. A method of generating a library of simulated-diffraction signals for an integrated circuit periodic grating, comprising:

generating sets of intermediate layer data,

wherein each set of intermediate layer data corresponds to one of a plurality of hypothetical layers of a hypothetical profile of the periodic grating;

storing the sets of intermediate layer data;

generating simulated-diffraction signals for a plurality of hypothetical profiles of the periodic grating based on the stored intermediate layer data; and

storing the simulated-diffraction signals.

15. The method of claim 14 ,

wherein generating sets of intermediate layer data comprises computing a wave-vector matrix for each set of intermediate layer data, and

wherein storing the sets of intermediate layer data comprises storing the wave-vector matrix generated for each set of intermediate layer data.

16. The method of claim 14 , wherein generating simulated-diffraction signals comprises:

constructing a matrix equation from the stored intermediate layer data corresponding to the hypothetical layers of the hypothetical profile; and

solving the constructed matrix equation to determine diffracted reflectivity values for the hypothetical profile.

17. The method of claim 14 , wherein generating simulated-diffraction signals comprises:

charaterizing the shape of a hypothetical profile of the periodic grating with a set of profile parameters; and

varying the set of profile parameters to generate the plurality of hypothetical profiles.

18. The method of claim 17 , wherein storing the simulated-diffraction signal comprises:

pairing each hypothetical profile with the simulated-diffraction signal generated for that hypothetical profile; and

storing the hypothetical profile and simulated-diffraction signal pair.

19. The method of claim 14 , wherein the intermediate layer data are stored in a computer memory, and wherein the simulated-diffraction signals are stored computer-readable medium.

20. The method of claim 14 comprising:

illuminating a portion of a semiconductor wafer with incident radiation

measuring a diffraction signal from the radiation diffracted from the portion of the semiconductor wafer; and

matching the measured diffraction signal with one of the stored simulated-diffraction signals.

21. The method of claim 20 , wherein the incident radiation includes light having a plurality of wavelengths, and wherein the portion of the wafer is illuminated from a single angle.

22. The method of claim 20 , wherein the incident radiation includes light having a single wavelength, and wherein the portion of the wafer is illuminated from a plurality of angles.

23. A computer readable medium having a library of simulated-diffraction signals generated in accordance with the method of claim 14 .

24. A method of using a library of simulated-diffraction signals to determine the profile of a periodic grating, the method comprising:

illuminating a portion of a semiconductor wafer with incident radiation;

measuring a diffraction signal from the radiation diffracted from the portion of the semiconductor wafer; and

matching the measured diffraction signal with one of a plurality of simulated-diffraction signals stored in a library of simulated-diffraction signals,

wherein the library of simulated-diffraction signals was generated in advance in accordance with the method of claim 14 .

25. A method of generating and using a library of simulated-diffraction signals of a periodic grating, the method comprising:

generating sets of intermediate layer data,

wherein each set of intermediate layer data corresponds to one of a plurality of hypothetical layers of a hypothetical profile of the periodic grating;

storing the sets of intermediate layer data;

generating simulated-diffraction signals for a plurality of hypothetical profiles of the periodic grating based on the stored intermediate layer data;

storing the simulated-diffraction signals;

illuminating a portion of a semiconductor wafer with incident radiation;

measuring a diffraction signal from the radiation diffracted from the portion of the semiconductor wafer; and

matching the measured diffraction signal with one of the stored simulated-diffraction signals.

26. A system for generating a library of simulated-diffraction signals for a periodic grating, comprising:

a processor configured to generate sets of intermediate layer data,

wherein each set of intermediate layer data corresponds to a hypothetical layer of a hypothetical profile of the periodic grating;

a memory configured to store the sets of intermediate layer data; and

wherein the processor is further configured to:

generate simulated-diffraction signals for a set of hypothetical profiles of the periodic grating based on the intermediate layer data stored in the memory.

27. The system of claim 26 , wherein the processor is further configured to compute a wave-vector matrix for each set of intermediate layer data, and wherein the wave-vector matrix is stored in the memory.

28. The system of claim 26 , wherein the processor is further configured to:

construct a matrix equation from the stored intermediate layer data corresponding to the hypothetical layers of a hypothetical profile; and

solve the constructed matrix equation to determine diffraction reflectivity values for the hypothetical profile.

29. The system of claim 26 further comprising:

a computer-readable medium configured to hold the generated simulated-diffraction signals.

30. A computer-readable storage medium containing computer executable instructions for causing a computer to generate a library of simulated-diffraction signals of a periodic grating, comprising instructions for:

generating sets of intermediate layer data,

wherein each set of intermediate layer data corresponds to one of a plurality of hypothetical layers of a hypothetical profile;

storing the sets of intermediate layer data;

generating simulated-diffraction signals for a plurality of hypothetical profiles of the periodic grating based on the stored intermediate layer data; and

storing the simulated-diffraction signals.

31. The computer-readable storage medium of claim 30 ,

wherein generating sets of intermediate layer data comprises computing a wave-vector matrix for each set of intermediate layer data, and

wherein storing the sets of intermediate layer data comprises storing the wave-vector matrix generated for each set of intermediate layer data.

32. The computer-readable storage medium of claim 30 , wherein generating simulated-diffraction signal, comprises:

constructing a matrix equation from the stored intermediate layer data corresponding to the hypothetical layers of the hypothetical profile; and

solving the constructed matrix equation to determine diffracted reflectivity values for the hypothetical profile.