Examining a structure formed on a semiconductor wafer using machine learning systems

1. A method of examining a structure formed on a semiconductor wafer, the method comprising:

a) obtaining a first diffraction signal measured from the structure using an optical metrology device;

b) inputting the first diffraction signal as an input to a first machine learning system;

c) after b), receiving a profile as an output of the first machine learning system with the first diffraction signal as the input to the first machine learning system, the profile having one or more parameters that characterize one or more features of the structure;

d) after c), inputting the profile as an input to a second machine learning system;

e) after d), receiving a second diffraction signal as an output of the second machine learning system with the profile as the input to the second machine learning system;

f) comparing the first diffraction signal to the second diffraction signal;

g) when the first and second diffraction signals match within one or more matching criteria, determining one or more features of the structure to be those characterized by the one or more parameters of the profile used as the input to the second machine learning system; and

h) when the first and second diffraction signals do not match within one or more matching criteria, altering one or more parameters of the profile and iterating steps d)-f) using the profile with the altered one or more parameters.

2. The method of claim 1 , wherein the one or more parameters of the profile include critical dimensions of the structure.

3. The method of claim 2 , wherein the critical dimensions include a top width or bottom width of the structure.

4. The method of claim 2 , wherein the critical dimensions include a height of the structure.

5. The method of claim 1 , wherein the one or more matching criteria include goodness of fit.

6. The method of claim 1 , wherein the one or more matching criteria include cost.

7. The method of claim 1 , wherein a local optimization algorithm is applied in iterating steps d)-f).

8. The method of claim 7 , wherein the local optimization algorithm is a Levenberg-Marquardt algorithm.

9. The method of claim 1 , wherein the second machine learning system was trained using a training process, the training process comprising:

obtaining a first set of training data, the first set of training data having profile and diffraction signal pairs; and

using the profile and diffraction signal pairs from the first set of training data to train the second machine learning system to generate a diffraction signal as an output for a profile received as an input.

10. The method of claim 9 , wherein the first machine learning system was trained using the training process, the training process further comprising:

generating a second set of training data using the second machine learning system after the second machine learning system has been trained using the first set of training data, the second set of training data having diffraction signal and profile pairs; and

using the diffraction signal and profile pairs from the second set of training data to train the first machine learning system to generate a profile as an output for a diffraction signal received as an input.

11. The method of claim 9 , wherein the diffraction signals in the first set of training data were generated using a modeling technique prior to training the first and second machine learning systems.

12. The method of claim 11 , wherein the modeling technique includes rigorous coupled wave analysis, integral method, Fresnel method, finite analysis, or modal analysis.

13. The method of claim 1 , wherein the first and second machine learning systems are neural networks.

14. A computer-readable storage medium containing computer executable instructions for causing a computer to examine a structure formed on a semiconductor wafer, comprising instructions for:

a) obtaining a first diffraction signal measured from the structure using an optical metrology device;

b) inputting the first diffraction signal as an input to a first machine learning system;

c) after b), receiving a profile as an output of the first machine learning system with the first diffraction signal as the input to the first machine learning system, the profile having one or more parameters that characterize one or more features of the structure;

d) after c), inputting the profile as an input to a second machine learning system;

e) after d), receiving a second diffraction signal as an output of the second machine learning system with the profile as the input to the second machine learning system;

f) comparing the first diffraction signal to the second diffraction signal;

g) when the first and second diffraction signals match within one or more matching criteria, determining one or more features of the structure to be those characterized by the one or more parameters of the profile used as the input to the second machine learning system; and

h) when the first and second diffraction signals do not match within one or more matching criteria, altering one or more parameters of the profile and iterating steps d)-f) using the profile with the altered one or more parameters.

15. The computer-readable storage medium of claim 14 , wherein the one or more parameters of the profile include critical dimensions of the structure.

16. The computer-readable storage medium of claim 15 , wherein the critical dimensions include a top width or bottom width of the structure.

17. The computer-readable storage medium of claim 14 , wherein a local optimization algorithm is applied in iterating steps d)-f).

18. A system to examine a structure formed on a semiconductor wafer, the system comprising:

a first machine learning system configured to receive a first diffraction signal and generate a profile as an output, wherein the profile includes one or more parameters that characterize one or more features of the structure;

a second machine learning system configured to receive the profile generated as the output from the first machine learning system and generate a second diffraction signal; and

a comparator configured to compare the first diffraction signal and the second diffraction signal, wherein one or more features of the structure are determined to be characterized by the one or more parameters of the profile when the first and second diffraction signals match within one or more matching criteria.

19. The system of claim 18 , further comprising:

an optimizer configured to apply an optimization algorithm to obtain a diffraction signal that matches the first diffraction signal within the one or more matching criteria.

20. The system of claim 18 , further comprising:

an optical metrology device configured to measure a diffraction signal from the structure, wherein the first diffraction signal received by the first machine learning system is measured using the optical metrology device.